Dan Hatton's Home Page

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Who I Am

Biography

My professional interests are: Much of the remainder of this page is dedicated to abstracts of published conference presentations, papers and reports on the above research work.

Professional Body Memberships

Publications

Peer-reviewed papers in journals

D. C. Hatton, P. R. Sammonds, and D. L. Feltham. "Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified". Philos. Mag. 89(31):2771-2799, Nov. 2009. doi:10.1080/14786430903113769

Abstract: Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

Full text for Philos. Mag. subscribers

Full text of author-generated postprint for everyone else

D. C. Hatton and A. W. Woods. "Diffusion-controlled dissolution of a binary solid into a ternary liquid with partially-molten zone formation". Proc. R. Soc. A 464(2094):1615-1637, Jun. 2008. doi:10.1098/rspa.2007.024

Abstract:We build a theoretical model of equilibrium dissolution of a homogeneous, solid mixture of two salts A and B, KCl and NaCl being used as the type example, into an aqueous solution of the two salts, with diffusive transport. We find that there are two sharp dissolution fronts, separating fluid, a partially molten zone containing a single solid and mixed solid. The phase change happens almost entirely at the two sharp fronts. In equilibrium, the leading front exhibits a small amount of precipitation of NaCl, simultaneous with complete dissolution of KCl. There is a unique surface in the space of far-field fluid KCl concentration, far-field fluid NaCl concentration and solid composition, dividing conditions where NaCl is the solid in the partially molten zone, from conditions where KCl is the solid in the partially molten zone. The movement rates of the dissolution fronts decrease as the concentration of either salt in the far-field fluid is increased. The movement rates of the dissolution fronts increase as either far-field temperature is increased, but this effect is smaller than that of concentration. In most circumstances, the dissolution front for a given salt moves more slowly, the more of that salt is present in the original solid, although the mass dissolution rate is not greatly affected by the solid composition.

Full text for Proc. R. Soc. A subscribers

Full text of author-generated postprint for everyone else

D. C. Hatton and A. W. Woods. "Compositional controls on melting and dissolving a salt into a ternary melt". Proc. R. Soc. A 463(2081):1211-1229, May 2007. doi:10.1098/rspa.2007.1819

Abstract:We explore theoretically the controls on dissolution of salt A, in an undersaturated brine of salts A and B. We show that, as the concentration of B increases, the dissolution rate of A decreases, for brine of given temperature. We also show that there is a sharper decrease in dissolution rate with increasing concentration, for concentrations of B above a critical value, where B limits the equilibrium concentration. We explore the implications of the predictions for dissolution of KCl or NaCl, by a mixed brine of NaCl and KCl, a common reaction that may arise in dissolution of evaporites. We predict that, with mixed-composition brine, KCl crystals dissolve more rapidly than NaCl crystals, unless the (far-field) brine is nearly saturated in KCl. We also predict that the dissolution rate of these salts is largely independent of fluid temperature and is controlled by compositional diffusion.

Full text for Proc. R. Soc. A subscribers

Full text of author-generated postprint (caution! contains typos!) for everyone else

P. D. Taylor, D. L. Feltham, P. R. Sammonds and D.[ C.] Hatton. "Continuum sea ice rheology determined from subcontinuum mechanics". J. Geophys. Res. 111(C11):C11015-1-C11015-14, Nov. 2006. doi:10.1029/2005JC002996

Abstract: A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.

Full text for J. Geophys. Res. C subscribers

W. S. Lew, S. P. Li, L. Lopez-Diaz, D. C. Hatton and J. A. C. Bland. "Mirror Domain Structures Induced by Interlayer Magnetic Wall Coupling". Phys. Rev. Lett. 90(21):217201-1-217201-4, May 2003. doi:10.1103/PhysRevLett.90.217201

Abstract: We have found that during giant magnetoresistance measurements in ~10x10 mm^2 NiFe/Cu/Co continuous film spin-valve structures, the resistance value suddenly drops to its absolute minimum during the NiFe reversal. The results reveal that the alignment of all magnetic domains in the NiFe film follow exactly that of corresponding domains in the Co film for an appropriate applied field strength. This phenomenon is caused by trapping of the NiFe domain walls through the magnetostatic interaction with the Co domain-wall stray fields. Consequently, the interlayer domain-wall coupling induces a mirror domain structure in the magnetic trilayer

Full text for Phys. Rev. Lett. subscribers

D. R. Westhead, D. C. Hatton and J. M. Thornton. "An atlas of protein topology cartoons available on the World-Wide Web". Trends Biochem. Sci. 23(1):35-36, Jan. 1998. doi:10.1016/S0968-0004(97)01161-4

Abstract (not part of original paper:) The three-dimensional structures of many proteins have recently been determined, by a variety of experimental techniques. These structural data are of relevance to the function and evolution of proteins; indeed, it has become clear that evolution changes structures much more slowly than it changes peptide sequences. Computational tools have become available for producing visual representations, which are simplified to varying degrees, of complicated three-dimensional protein structures. At the simplest end of the spectrum are protein topology cartoons, which represent the relative positions of secondary structure elements, projected in a two-dimensional plane, along with a direction, perpendicular to the plane, assigned to each secondary structure element. The algorithm of Flores et al. (T. P. Flores, D. M. Moss, and J. M. Thornton. An Algorithm for Automatically Generating Protein Topology Cartoons. Protein Eng., 1994,) as implemented in the computer program TOPS, automates the production of one particular variety (M. J. E. Sternberg and J. M. Thornton. On the conformation of proteins: the handedness of the connection between parallel beta-strands. J. Mol. Biol., 1977) of cartoon. The cartoon representation eases visual identification of structural motifs such as the Greek key or the beta sandwich.

A protein topology web site has been created, containing information about protein structural topology, as well as an atlas of topology cartoons. In the atlas, every poly-peptide chain of more than 30 residues in the 1st July 1997 release of the Brookhaven Protein Data Bank is represented, by the cartoon of a chain to which it has at least 95% sequence similarity, which is believed to imply identical topology in almost all cases. Extensive modifications were made to the TOPS program, which, as visual comparison with the three-dimensional structures revealed, increased the proportion of the cartoons which represented the structures well enough to require no manual redrawing, to 82%.

The web site includes a server, which generates topology cartoons for user-submitted protein structures. It is intended to maintain the atlas and server, in conjunction with the macromolecular structure database and the mirror of the Brookhaven Protein Data Bank, at the European Bioinformatics Institute.

Full text for Trends Biochem. Sci. subscribers

Peer-reviewed papers in conference proceedings

P.[ R.] Sammonds, D.[ C.] Hatton, D.[ L.] Feltham and P.[ D.] Taylor. "Experimental Study of Sliding Friction and Stick-Slip on Faults in Floating Ice Sheets". In Proceedings of the 18th International Conference on Port and Ocean Engineering Under Arctic Conditions, vol. 1, Clarkson University, Potsdam, New York, Jun. 29 2005, pp. 303-312. ISBN: 0964788810

Abstract:We have undertaken double-direct-shear friction experiments with floating ice sheets. These tests have been done at the ice basins at HSVA, Hamburg and the Helsinki University of Technology (HUT). Floating ice blocks are pushed past each other, with slip displacement, stress and acoustic emissions monitored at the interfaces. We have therefore measured the effect of frictional sliding on simulated faults. Mostly the sliding took a stick-slip form. The velocity and shear stress are non-uniform in space as well as in time. Measurements of the same stick-slip cycle, at several positions along the fault, allow us to identify a nucleation zone, which begins to slip before the rest of the fault and to relate this spatial variation of velocity and the temporal variation of shear stress; the slipping region, therefore, behaves like a wave-packet, propagating away from the nucleation zone.

Full volume of proceedings

D. L. Feltham, P. R. Sammonds and D. C. Hatton. "Method of determining a geophysical-scale sea ice rheology from laboratory experiments". In Proceedings of the 16th IAHR Symposium on Ice, vol. 3, International Association of Hydraulic Engineering and Research, Dec. 2002.

Abstract: We present a methodology that allows a sea ice rheology, suitable for use in a General Circulation Model (GCM), to be determined from laboratory and tank experiments on sea ice when combined with a kinematic model of deformation. The laboratory experiments determine a material rheology for sea ice, and would investigate a non- linear friction law of the form t proportional to s2/3, instead of the more familiar Amonton's law, t = ms (t is the shear stress, m is the coefficient of friction and s is the normal stress). The modelling approach considers a representative region R containing ice floes (or floe aggregates), separated by flaws. The deformation of R is imposed and the motion of the floes determined using a kinematic model, which will be motivated from SAR observations. Deformation of the flaws is inferred from the floe motion and stress determined from the material rheology. The stress over R is then determined from the area-weighted contribution from flaws and floes.

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Invited lectures at conferences

D.[ C.] Hatton, P.[ R.] Sammonds, D.[ L.] Feltham and P.[ D.] Taylor. "Micro-mechanical modelling of ice internal friction". Invited lecture, ESF Micro-DICE Workshop on Sea and Marine Ice Processes, London, Nov. 8 2010

Abstract: Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. These two principles are justified by reference to equilibrium thermodynamics and physical kinetics, respectively. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

Conference posters with print abstracts

P. D. Taylor, D. L. Feltham, P.[ R.] Sammonds and D.[ C.] Hatton. "Sea ice rheology and the sub-grid scale". Eos Trans. Am. Geophys. Union 88(52, Fall Meeting supplement):Abstract C11B-0444, Dec 2007.

Abstract: The sea ice component of global climate models (GCMs) must contain representations of sea ice stress appropriate to their spatial grid resolution. We explore the relationship between the sea ice stress and sub-grid scale floe and lead interaction using a clearly defined methodology. The calculation of GCM sea ice stress depends upon the assumed mechanical behaviour of sea ice, the geometry of floes and leads, and the manner in which a collection of floes and leads deform in response to large-scale atmospheric and oceanic forcing. We discuss the sensitivity of GCM sea ice stress to the sub-grid scale sea ice state, calculations using Radarsat SAR data coincident with the SHEBA site, and implications for sea ice modelling.

University theses and reports

H. E. Huppert, M. J. Golding, M. A. Hallworth, D. C. Hatton, J. A. Neufeld and D. Vella. Framework for development of clean coal: consultation response. Response to UK government consultation, University of Cambridge, Institute of Theoretical Geophysics, Sep. 2010.

Executive summary: We welcome the broad thrust of the draft framework for the development of clean coal. We are particularly pleased to note the emphasis on a diverse range of measures for mitigating climate change, the recognition that both market-based and regulatory approaches to encouraging the deployment of CCS are valuable, and the suggestion that the proposed requirement to demonstrate CCS should apply immediately.

We make several suggestions on matters of detail in response to the consultation questions. Specifically, we suggest the establishment of a process of continual review of the realistic capacity of carbon dioxide storage reservoirs. We further suggest that, to allow for the rapid rate of generation of new scientific information, the following are needed. First, an explicit, quantitative statement of the timescale that government considers sufficient for a reservoir to store carbon dioxide securely. Second, an explicit, quantitative statement of the level of leakage risk that government considers acceptable. Third, the publication of plans to accelerate the release into the public domain of seismic, borehole log, well injection test, and drilling record data generated by the private sector. Fourth, an explicit statement of government's view on the extent to which bio-fuel power stations should be covered by regulations requiring carbon capture readiness. Finally, the production of a companion document establishing similar principles for the retrofit of carbon capture and storage systems at existing power stations. We also note the importance of potential CCS operators having robust plans for monitoring their storage reservoirs, using monitoring technologies that have been thoroughly demonstrated to be of sufficient accuracy and precision.

In addition to these technical matters, we make several suggestions about the financial and regulatory aspects of the path to CCS deployment. First, we urge the early production by government of detailed criteria for deciding whether CCS is technically and economically proven. Second, we suggest the adoption of measures to counter any disincentives to private-sector funding of carbon capture and storage research. Third, we point out that the judgement as to whether CCS is technically and economically proven may need to be a continual and site-by-site process, starting as soon as reasonably practicable. Fourth, we propose that the starting date for the requirement to retrofit be left open (but certainly no later than 2025). This will allow for flexibility should CCS be technically and economically proven in advance of 2020. Fifth, we suggest that the proposed levy on electricity suppliers could be linked to carbon emissions. Sixth, we urge further consideration of the relative positions of coal and natural gas, with respect to the requirement to retrofit. Seventh, we ask for a more detailed definition of the crucial phrase ``best attainable standards'' for judging the efficiency of existing power stations proposed as CCS demonstration sites. Eighth, we suggest that it may be helpful if public funding for demonstration projects is protected from late-stage withdrawal through the spending review. Ninth, as an alternative to the proposed requirement to cease operation of power plants that fail to operate the CCS chain, we propose a mechanism for government to take over the running of such plants. Tenth, we urge extra care to be taken over the equity implications of co-location of demonstration projects. Finally, we note that it may be useful to address the rôle of perceived risk in suppressing private CCS investment as part of a wider review of how government can influence levels of risk aversion in the investment capital markets.

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H. E. Huppert, M. J. Golding, M. A. Hallworth, D. C. Hatton, J. A. Neufeld and D. Vella. Guidance on Carbon Capture Readiness and Applications under Section 36 of the Electricity Act 1989: consultation response. Response to UK government consultation, University of Cambridge, Institute of Theoretical Geophysics, Jun. 2009.

Executive summary: We welcome the broad thrust of the DECC's draft guidance document on carbon capture readiness at new power stations, and of the Secretary of State's proposals for additional requirements for carbon capture and storage. We suggest several clarifications that could usefully be provided, either in the guidance document, or in subsidiary documents. Specifically, we suggest the establishment of a process of continual review of the realistic capacity of carbon dioxide storage reservoirs and the criteria for introducing new carbon storage reservoirs. We further suggest that to allow for the rapid rate of generation of new scientific information, the following are needed. First, an explicit, quantitative statement of the timescale that government considers sufficient for a reservoir to store carbon dioxide securely. Second, the inclusion in the guidance document of plans to accelerate the release into the public domain of seismic, borehole log, well injection test, and drilling record data generated by the private sector. Third, an explicit statement of government's view on the extent to which bio-fuel power stations should be covered by regulations requiring carbon capture readiness. Finally, the production of a companion document giving similar guidance for the retro-fitting of carbon capture and storage systems at existing power stations. We also suggest that the guidance document could benefit from being updated in a number of ways, in the light of the Secretary of State's additional proposals. Specifically, we suggest that, if different regulations are to apply to coal and natural gas, it would be useful for the guidance document to mention the two fuels separately. If some electricity generators are to be required to undertake carbon capture and storage from start-up of new facilities, the advice in the guidance document, that they do not need to commit themselves to using a particular storage reservoir at that stage, is no longer correct. The guidance document could usefully include measures to counter any disincentives to private-sector funding of carbon capture and storage research. We propose that the same review process that continually reassesses the realistic capacity of carbon dioxide storage reservoirs and the criteria for introducing new carbon storage reservoirs, may also need to keep under continual review the list of issues that applicants for power station construction permits can usefully address. Finally, we suggest that it would be helpful for applicants to provide details of their plans for monitoring of CO2 during and after its injection into a reservoir.

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D. C. Hatton. Spin-Polarized Electron Scattering at Ferromagnetic Interfaces. Ph.D. thesis, University of Cambridge, Girton College, Aug. 2003.

Abstract: A theory of polarized electron reflection, at the surface of a magnetic material, is devised, predicting that the rate of electrons leaving the surface will be

\begin{displaymath} G = \left(\frac{e^2V^2}{16E_b^2\cos^4I}+\frac{e^2\hbar^2B^2}{192m_e^2E_b^2\cos^4I}\right)\frac{F}{e}\textrm{,} \end{displaymath} (1)

and that the reflected beam's polarization will be
\begin{displaymath} P = -\frac{4e^2\hbar{}m_eVB}{12e^2m_e^2V^2+e^2\hbar^2B^2}\textrm{.} \end{displaymath} (2)

$V$ represents the electrostatic potential inside the material, $B$ the Weiss field inside the material, $I$ the angle of incidence of the electron beam, $E_b$ each incident electron's kinetic energy, and $F/e$ the rate of electron incidence. The equations represent a lowest order Taylor expansion in $\frac{1}{E_b}$, which, for cobalt samples, renders them applicable as long as $E_b \gg{} \sim{}700\,\mathrm{meV}$. They also involve an assumption that that the topmost layer of the sample has a thickness $\gg{} 1\,\mathrm{nm}$.

Measurements are presented of spin-correlated electron arrival rates at a Mott-polarimeter's two detectors, from the reflected electron beam from $Co/Cu(001)$, as a function of cobalt thickness, incident energy, and incident intensity. Example results are displayed graphically in chapter 5. They are analysed using three distinct methodologies.

  1. Visual inspection of the data is used to make qualitative suggestions about future directions for modelling of electron reflection processes at magnetic surfaces. A magnetization-dependent systematic error is discovered in electron arrival rates at the polarimeter's detectors, and is tentatively attributed to the deflection of the electron beam by a stray magnetic field, from the sample, or from some part of the sample holder. This raises the possibility, for the future, of using a reflected electron beam's spatial deflection, rather than its spin polarization, to characterize magnetic samples.
  2. A traditional estimator of the Mott asymmetry, associated with the reflected polarization, is calculated for each combination of film thickness, incident energy, and incident intensity. Results are displayed graphically in section 5.2. The polarizations of most reflected beams from cobalt films are clearly non-zero, indicating that the experiment has successfully detected the cobalt's Weiss field. Quantitative determination of this polarization is, however, rather imprecise, and there is a puzzling non-zero asymmetry from the bare copper surface.
  3. It is argued that the accuracy of the traditional estimator may be compromised by its non-linearity in the electron arrival rates; therefore, Bayesian inference is used to estimate the parameters in two adaptive models, based on the above theory, and to estimate relative probabilities for these models, equipped with the data. One model has a non-zero Weiss field in the films, the other does not. Results of the parameter estimation are displayed graphically in sections 5.3.2 and 5.3.3; quantitative estimation of the sample properties is, as for the traditional estimator, rather imprecise. The data are found to rule out a null hypothesis, in which the cobalt's Weiss field is zero, very strongly, leaving it with a posterior probability of $0.34\times{}10^{-2014444631}$ , indicating firmly that the experiment has successfully detected the cobalt's Weiss field.

These measurements were preceded by a process (sections 5.4, 5.5) of trial and error, in which attempted measurements of the spin polarization of reflected electron beams revealed sources of systematic error, which were addressed by adaptations to the polarimeter, and to the experimental technique.

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D. C. Hatton. Mott Polarimetry at the Cavendish Laboratory. First year report, University of Cambridge, Dec. 2000.

Abstract (not part of original report:) A number of technical difficulties have been overcome, with the result that the spin polarization of a reflected electron beam, from a magnetic multi-layer, has been successfully measured.

The multi-layer structure $0.5ML$ $Mn/6ML$ $Co/Cu(001)$ forms (B.-Ch. Choi, P. J. Bode, and J. A. C. Bland. Formation of a two-dimensional $c(2\times 2)\: Mn-Co(001)$ ferromagnetic surface alloy on $Cu(001)$. Phys. Rev. B, 1998; B.-Ch. Choi, P. J. Bode, and J. A. C. Bland. Magnetic anisotropy strength and surface alloy formation in $Mn/Co/Cu(001)$ overlayers. Phys. Rev. B, 1999; Structure and magnetic properties of a two-dimensional $c(2\times 2)\: Mn-Co/Cu(001)$ surface alloy. J. Appl. Phys., 1999) an unusual, ordered surface alloy of manganese and cobalt, the magnetic configuration of which is (A. Noguera, S. Bouarab, A. Mokrani, C. Demangeat, and H. Dreyssé. Very thin $Mn$ films on fcc $Co(001)$. J. Magn. Magn. Mater., 1996) an issue of controversy.

Polarized electron reflection can provide an indicator of the magnetization of the alloy, independent of the methods which have previously been brought to bear thereon. To this end, the polarizations of reflected electron beams at three energies from a $10ML\: Cu/0.5ML\: Mn/7ML\: Co/Cu(001)$ sample have been measured.

The Mott polarimeter ,as improved by the measures described below, was used to measure the polarization of the specularly reflected electron beam (figure 3.3) from a $Cu/0.5ML$ $Mn/7ML$ $Co/Cu$ magnetic multilayer (figure 3.4) grown by MBE.

Figure 3.3: The Geometry Used for the Polarization Analysis of the Specularly Reflected Beam from $Cu/0.5ML$ $Mn/7ML$ $Co/Cu$
\begin{figure}$\quad$\\ $\quad$\\ \epsfxsize =15cm \epsfysize =11cm \epsffile{geometry.eps}\end{figure}

Figure 3.4: Schematic of the Magnetic Multilayer Sample Used in the Polarimetry Experiments. The Clear Distinction Shown between the Manganese and Cobalt Layers Is Not Representative of the Ordered Alloying Revealed by LEED for This Sample, and Used To Calibrate the $Mn$ Thickness
\begin{figure}$\quad$\\ $\quad$\\ \epsfxsize =15cm \epsfysize =11cm \epsffile{surface.eps}\end{figure}

Under certain assumptions, and with the use of a range of experimental and mathematical techniques, designed to eliminate systematic errors, the measured left-right scattering asymmetries, representative of the reflected polarizations, were as shown in figure 3.6.

Figure 3.6: Relative Polarization ($SP$) Measurements Obtained Using Formula for Multiplicative Systematic Error Elimination for Each Run of the Experiment
\begin{figure}$\quad$\\ $\quad$\\ \epsfxsize =15cm \epsfysize =11cm \epsffile{polarization.eps}\end{figure}

It can be inferred from the non-zero polarization values (figure 3.6) that the part of the multilayer structure (figure 3.4) within the penetration depth of the electron beam has a non-zero magnetization component along $[100]$ in the remanent state after application of a strong magnetic field in the $\pm [100]$ direction. This does not, of itself, demonstrate that the manganese and cobalt layers have parallel magnetizations, nor that the manganese layer is internally ferromagnetic. It does, however, demonstrate the feasibility of similar experiments which will be capable of settling these issues.

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Articles in academic magazines and newsletters

D. R. Gilbert, D. R. Westhead, D. C.] Hatton and J. M. Thornton. "Pattern Searching over the TOPS Protein Topology Database". PDB Q. Newsl. (85):7-9, Jul. 1998.

Abstract: We have developed a system that supports fast pattern searching over TOPS protein topology databases; the facility is available at the TOPS protein structural topology WWW site(1) at http://tops.ebi.ac.uk/tops. The search engine is based on a string-graph algorithm and uses constraint propagation to prune the search space. Users can search on motifs from a library or define their own search patterns. All 15400 descriptions of protein domains currently in the Brookhaven Protein Data Bank (April 1998) have been converted into a database of TOPS diagrams (11MB). Average match times are 3-5ms per diagram on a Dec-Alpha. For example, it takes 80 seconds to find all matches to a jelly- roll type 1 description (500 hits out of 15400) on a Dec-Alpha. Some queries take advantage of precompiled topological information generated by the TOPS program; a search for Tim barrels takes 15 seconds to find 260 matches in the database. Load times are additionally 3 sec for the atlas and 32 sec for the PDB. Users can search on motifs from a library or define their own search patterns. We are now in the process of enhancing the system to permit users to compare the topology of a given domain with all the other domains in a database.

D. R. Westhead, D. C. Hatton, D. R. Gilbert and J. M. Thornton. "A WWW site devoted to protein structural topology". embnet.news 5(2), Jun. 1998

Abstract: We have recently set up a WWW site (D. R. Westhead, D. C. Hatton, and J. M. Thornton. An atlas of protein topology cartoons available on the World-Wide Web. Trends Biochem. Sci., 1998) devoted to protein structural topology. The most important service available on this site is an atlas of protein topology (TOPS) cartoons, in which most of the structures in the Brookhaven data bank (F. C. Bernstein, T. F. Koetzle, G. J. B. Williams, E. F. Meyer Jr., M. D. Brice, J. R. Rodgers, O. Kennard, T. Shimanouchi, and M. Tasumi. The Protein Data Bank: a computer-based archival file for macromolecular structures. J. Mol. Biol., 1977) (PDB) are represented. There is also a "server" to which protein structures can be submitted for topology cartoon calculation and HTML pages explaining the topology cartoons and giving information about protein structural topology in general.  In addition, users can search them in atlas, or a  TOPS version of the PDB, using motifs from a library or by defining their own search patterns.

Protein three dimensional folds can be complicated and difficult to interpret. Protein topology cartoons are a graphical form of simple two dimensional schematic diagrams whose aim is to simplify folds so that they can be more easily understood and compared. They represent a fold as a sequence of secondary structure elements and hold information about their relative orientation and spatial position. An example cartoon is shown in figure 1. Information about its interpretation is given in the caption. The topology cartoon shows the beta sandwich structure of the fold with the relative spatial and sequential positions of the constituent strands. This is much more clear than the equivalent three dimensional structure.

D. R. Westhead, D. C. Hatton and J. M. Thornton. "Protein Topology WWW Site". PDB Q. Newsl. (83):8, Jan. 1998

Abstract (not part of original article:) A protein topology web site has been created, containing information about protein structural topology, as well as an atlas of topology cartoons. The web site includes a server, which generates topology cartoons for user-submitted protein structures. Protein topology cartoons are simplified diagrammatic representations of the structures of protein molecules, which represent the relative positions of secondary structure elements, projected in a two-dimensional plane, along with a direction, perpendicular to the plane, assigned to each secondary structure element. The simplified nature of the cartoons is intended to facilitate understanding and comparison of the protein structures.

In the atlas, every poly-peptide chain of 30 or more residues in the 1st July 1997 release of the Brookhaven Protein Data Bank is represented, by the cartoon of a chain to which it has at least 95% sequence similarity. Extensive modifications were made to the TOPS program, which, as visual comparison with the three-dimensional structures revealed, increased the proportion of the cartoons which represented the structures well enough to require no manual redrawing, to 82%.

At present, access to the atlas is through Java applets on the web pages. Future plans include making a Java-free version of the atlas available, and maintaining the atlas to allow for changes in the content of the PDB.

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Conference presentations without print proceedings

D.[ C.] Hatton and A.[ W.] Woods. "Ablation - and maybe growth - at the base of floating ice sheets". Conference presentation, ESF Micro-DICE Workshop on Sea and Marine Ice Processes, London, Nov. 9 2010

Abstract: Changes in the extent and volume of sea ice can disrupt regional and global temperature, alter ocean circulation, and affect sensitive ecosystems. Therefore, it is important to understand the physics by which sea ice ablates (or grows) at its base. Theoretical modelling of this process is a very well-studied problem, and we take as a starting point a model from the literature, based on phase equilibrium at the ice/fluid interface; heat balance between turbulent transport in fluid, conductive transport in ice, and latent heat consumption in ablation; and salt balance between turbulent transport in fluid and salt consumption in ablation. The model uses a linear temperature profile in the ice, meaning conductive heat transport inversely proportional to ice thickness. This makes thin ice tend to grow and thick ice tend to ablate. We note properties of the model not emphasized in the literature: the thickness-dependence of heat transport gives ice a surprisingly small equilibrium thickness, which it approaches on a surprisingly rapid relaxation timescale. We suggest a refinement to the model, based on the idea that the ice base has imperfect information about the thickness of ice above it, which brings the model into closer agreement with field data on ablation rates. We note, however, that neither the original nor the refined model can fully explain how ice of typical field thicknesses grows. We speculate on the possibility that, at certain times, diffusive transport dominates over turbulent transport in the fluid, and on whether this can explain the growth of thick ice.

D. C. Hatton, R. Rabe, P. R. Sammonds, P. D. Taylor and D. L. Feltham. "Experimental Study of Sliding Friction and Stick-Slip on Faults in Floating Ice Sheets". Conference presentation, UK Sea Ice Specialists' Meeting, Cambridge, Sep. 28 2004

Abstract: With the aim of incorporating, into geophysical-scale sea-ice models, and thence into climate-predicting general circulation models, the effect, on the ice stress-strain relationship, of frictional sliding on faults, we have undertaken double-direct-shear friction experiments, with floating ice sheets.

Mostly, the sliding took a stick-slip form: sliding velocity and shear stress, at a given position on the fault, were episodically time-dependent, shear stress dropping as sliding accelerated.

When we seek a local, instantaneous friction law, this militates in favour of proposed laws, in which the shear stress decreases with increasing speed, and against those, in which the shear-stress is velocity-independent or grows with increasing speed. We can test friction laws further by plotting the measurements, in combinations of variables, for which each proposed law predicts a simple graphical form.

The velocity and shear stress are non-uniform in space as well as in time. Measurements of the same stick-slip cycle, at several positions along the fault, allow us to identify a nucleation zone, which begins to slip before the rest of the fault, and to relate this spatial variation of velocity and the temporal variation of shear stress; the slipping region, therefore, behaves like a wave-packet, propagating away from the nucleation zone.

P.[ R.] Sammonds, D.[ C.] Hatton, D.[ L.] Feltham and P.[ D.] Taylor. "Slip weakening model for Arctic sea ice dynamics". Conference presentation, UK Sea Ice Specialists' Meeting, Cambridge, Sep. 28 2004

Abstract: We have studied slip-weakening behaviour in laboratory and ice tank experiments in ice. We propose that sea ice dynamics is dominated by tensile fracture and frictional slip. Further, stick-slip behaviour, which has only recently been recognised by us, we believe to be an important deformation mechanism. We proposed that the slip-weakening model can capture the essential mechanical properties of ice in shear, including the transition from brittle to ductile behaviour with increasing normal stress and temperature, and the transition from stable frictional sliding to stick-slip behaviour, necessary for modelling sea ice dynamics.

D. C. Hatton and J. A. C. Bland. "Classical-Field Theory of Electron Waves as a Polarized Radiation Probe of Magnetic Surfaces". Conference presentation number C31.1.3, CMD19CMMP 2002, Apr. 8 2002.

Abstract: Recently, there has been a revival (W. Weber, D. Oberli, S. Riesen, and H. C. Siegmann. The electron analogue to the Faraday rotation. New J. Phys., 1999) of interest (C. G. Darwin. On the Diffraction of the Magnetic Electron. P. Roy. Soc. Lond. A Mat., 1928) in mechanisms for changing the spin polarization of an electron beam on transmission through, or reflection from, a magnetic surface. An understanding of these mechanisms would (W. Weber, D. Oberli, S. Riesen, and H. C. Siegmann. The electron analogue to the Faraday rotation. New J. Phys., 1999) allow the use of an electron beam as a polarized radiation probe for magnetic characterization, like light in MOKE and neutrons in PNR. Here, a mechanism is described which, unlike simultaneously occurring processes proposed elsewhere (W. Weber, D. Oberli, S. Riesen, and H. C. Siegmann. The electron analogue to the Faraday rotation. New J. Phys., 1999,) polarizes an unpolarized incident beam without recourse to inelastic processes.

A magnetic field leads to a Zeeman term in an electron's Hamiltonian, which depends on the angle $\theta$ between the electron's spin vector and the magnetic flux. As a result, when an electron wave is incident on the surface of a bulk magnetic material (figure 1,) the wave-number of the transmitted wave depends on $\theta$. When the conditions of continuity of the wave-function, and of its first spatial derivative, at the surface, and conservation of particles, are applied, an electron reflection coefficient is obtained which also depends on $\theta$. Therefore, some polarizations are preferentially reflected, while others are preferentially transmitted. The amplitude reflection and transmission coefficients can readily be converted to intensity coefficients, and averaged over an incoherent superposition of electron waves of different $\theta$, e.g. an unpolarized incident beam. The reflected polarization is

\begin{displaymath} P = -\frac{2e\mu_BVB}{3e^2V^2+\mu_B^2B^2}\textrm{,} \end{displaymath} (1)

which can take values
\begin{displaymath} -\frac{1}{\sqrt{3}}\leq{}P\leq\frac{1}{\sqrt{3}}\textrm{,} \end{displaymath} (2)

depending on the balance between $V$ and $B$.

The analysis can be extended to multi-layers using the theory of Fabry-Perot etalons.

Figure 1: Surface of a Bulk Magnetic Sample
\includegraphics[width=\textwidth, height=0.75\textwidth]{dhatton1}

: Full transcript

Web article

D. C. Hatton. "Some Philosophical Implications of Bayesian Statistics: Departure from Positivism and Association with Standpoint Epistemology". World-wide web page, Jun. 2004.

Short Abstract: Bayesians perform inference by applying Bayes' theorem

\begin{displaymath} P(T\vert E)=\frac{P(E\vert T)P(T)}{P(E)}\textrm{,} \end{displaymath} (1)

where the prior probability $P(T)$ represents the degree of belief in theory $T$, from a set $S$ of available theories, before the occurrence of evidence $E$, the posterior probability $P(T\vert E)$ represents the degree of belief in $T$ after the occurrence of $E$, the likelihood $P(E\vert T)$ is the probability that $T$ assigns to the occurrence of $E$, and $P(E) = \sum_{T\in{}S}P(E\vert T)P(T)$.

The Bayesian world-view is found to differ from positivism in four ways. Firstly, the positivist Occam's razor insists that $P(T) = P_0\epsilon{}^n$, where $n$ is the number of postulates in $T$, and $P_0$ is a normalizing constant to ensure $\sum_{T\in{}S}P(T) = 1$, whereas in the Bayesian view, $P(T)$ is a subjective and arbitrary choice. Secondly, positivism prohibits the entry of prescriptive ideologies into knowledge, whereas Bayes' theorem allows inferences to be drawn about prescriptive ideologies and descriptive theories alike. Thirdly, a prohibition on theories $T$, for which one cannot conceive of any evidence $E$, for which $P(E\vert T) = 0$, is sometimes associated with positivism, whereas Bayesian analysis can assess many such theories. Fourthly, any positivist prohibition on the consideration of evidence obtained with an ideology in mind is another example of insistence on the assignment of particular values to prior probabilities. Therefore, Bayesians, like standpoint epistemologists, will think such a prohibition inappropriate.

Bayesians view subjectivity as entering, inevitably, into academic study by four routes. Firstly, Bayesian inference cannot be performed without the use of a prior probability distribution, mirroring standpoint epistemologists' view that previous experience always affects the interpretation of evidence. For a Bayesian, the choice of prior probability distribution is arbitrary and subjective, and any attempt to achieve objectivity by claiming that a particular prior probability distribution is correct conceals this subjective choice, and renders it immutable. Bayesians conceptualize objectivity as the achievement of similar posterior probability distributions, from a range of prior probability distributions, mirroring standpoint epistemologists' view that theoretical beliefs need to be grounded by combining the conclusions of researchers with diverse previous experiences. If evidence has been noted, for which some theories have not produced likelihood values, a prior probability distribution can be devised that approximates the posterior probability distribution that the previous evidence would have produced, mirroring standpoint epistemologists' view that thinking on the basis of evidence, which has been obtained in the course of a marginalized lives, can improve the ability of researchers to interpret other evidence, whether or not they themselves experienced those marginalized lives.

Secondly, the Bayesian statistical decision theory uses the expected reduction, which an experiment will bring about, in an uncertainty function of the prior or posterior probability distribution, to judge the worth of an experiment, and therefore to choose experiments. It can be shown that every uncertainty function is associated with an ideology, for which it measures how much an experiment's results can improve the making of policy choices to implement that ideology. Bayesians may, therefore, suspect that claims that a particular piece of research is free of ideology conceal the inevitable influence of ideology in the selection of its experiments. This suspicion is shared with standpoint epistemology, and proponents of both traditions prefer to be open about the ideological motivation of their research.

Thirdly, ideology may also enter into academic study through attempts to produce a posterior probability distribution, in which the policy that will minimize the expectation of one's own loss function is the same policy that will minimize the expectation of the loss function of someone else with decision-making power. This possibility, against which Bayesian thinking can provide some protection, has been noted by standpoint epistemologists, as an abuse of science.

Fourthly, the prior probability distribution can affect the posterior probability distribution through experiment selection. In a toy problem, it is found that whichever of two theories has the higher prior probability is able to make an experiment that confirms it appear to be the most interesting experiment to undertake, and thereby to enhance its probability. This may be related to certain recent epistemological observations, outside of the standpoint epistemology tradition.

Physicists have a tendency to study phenomena at very large and very small length scales. This can be modelled as the result of experiment selection, under statistical decision theory, using a greedy top-down approximation to the Shannon entropy as the uncertainty function.

Full text

Courses I've Taught

Asymptotic Methods

I currently provide small-group classes in Asymptotic Methods, within the third-year undergraduate Mathematics programme at the University of Cambridge, on behalf of various colleges of the University (Jesus College; Pembroke College; Gonville and Caius College; Corpus Christi College; Selwyn College; Homerton College; and St. Edmund's College). There follow links to some resources for this course:

Fluid Dynamics

I have also recently provided small-group classes in Fluid Dynamics, within the second-year undergraduate Mathematics programme at the University of Cambridge, on behalf of Newnham College. There follow links to some resources for this course:

Classical Dynamics and Fluids

Previously, I have given small-group classes in Classical Dynamics and Fluids, within the Physics B option of the second-year undergraduate Natural Sciences programme at the University of Cambridge, on behalf of Peterhouse. There follow links to some resources for this course:

Other courses

I've also previously taught several other courses:

History of this page.

E-mail Dan Hatton.

Copyright Daniel C. Hatton 2001-2012. Details of copyright.