nouvo
Recent publications
Stephen T. Hyde
and colleagues
(Applied Mathematics Dept, Physics, Australian National University)
...
like life, this page mutates in fits and starts ...
(last edited February 10, 2011)
A chronological list of papers, book chapters, books etc, is available here as a pdf file.
A rough classification by
topic is shown below
Relevant graphical logos are appended to each paper






Nets
Networks
Embedded Graphs
Tangled Patterns

Biominerals and biomaterials
"Biomorphs":
living vs. dead matter

Cellular structures, surfaces 
"Hard"
framework materials:
Zeolites
Metalloorganic frameworks
Novel
carbon nanofoam etc. 
Soft
matter:
Lyotropic liquid crystals microemulsions
block
copolymers
Membranes in vivo

Theoretical
crystallography

PDF files
are available for private use only as they are copyrighted
 T Castle, M Evans and S T Hyde, “Entanglement of embedded graphs”, to be published (2011).
pdf
version (1.2 MB)
Abstract:
We discuss the identiﬁcation of untangled graph embeddings for ﬁnite planar and non
planar graphs as well as inﬁnite crystallographic nets. Two parallel approaches are discussed:
explicit 3space embeddings and reticulations of 2manifolds. 2D and 3D energies are pro
posed that allow ranking of (un)tangled embedded graphs.
 M. Saba, M. Thiel , M.D. Turner, S.T. Hyde, M. Gu, K. GrosseBrauckmann, D.N. Neshev, K. Mecke, and G.E. SchröderTurk, “Circular dichroism in biological photonic crystals and cubic chiral nets”, Phys Rev Lett, in press (2011).
Abstract:
Nature provides impressive examples of chiral photonic crystals, with the notable example of the
cubic srs network structure realized in wingscales of several butterﬂy species. By a novel circular
polarization analysis of the band structure of such networks, we demonstrate strong circular dichro
ism eﬀects: The butterﬂy srs microstructure, of cubic I 41 32 symmetry, shows signiﬁcant circular
dichroism for blue to ultraviolet light, that warrants a search for biological receptors sensitive to
circular polarization. A derived synthetic structure based on four likehanded silicon srs nets ex
hibits a large circular polarization stop band of width exceeding 30%. These ﬁndings oﬀer design
principles for chiral photonic devices.
 G.E. SchröderTurk, S. Wickham, H. Averdunk, F. Brink, J.D. Fitz Gerald, L. Poladian, M.C.J. Large and S.T. Hyde, “The chiral structure of porous chitin within the wingscales of Callophrys rubi”, J Struct Biol, in press (2011). DOI: 10.1016/j.jsb.2011.01.004
pdf
version (1.1 MB)
Abstract:
The structure of the porous
threedimensional reticulated pattern in the wing scales of the
butterﬂy C. rubi (the Green Hairstreak)
is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a fragment of
this material reveals that the predominantly chitin material is assembled in the wing scale to form a structure whose geometry
bears a remarkable correspondence to the srs net, wellknown in solid
state chemistry and soft materials science. The porous solid
is bounded to an excellent approximation by a parallel/cmc surface to the Gyroid, a threeperiodic minimal surface with cubic
crystallographic symmetry I 41 32, as foreshadowed by Stavenga and Michielson. The scale of the structure is commensurate with
the wavelength of visible light, with an edge of the conventional cubic
unit cell of the cmcGyroid of approximately 310 nm. The
genesis of this structure is discussed, and we suggest it aﬀords a
remarkable example of templating of a chiral material via soft
matter, analogous to the formation of mesoporous silica via surfactant
assemblies in solution. In the butterﬂy, the templating is
achieved by the lipidprotein membranes within the smooth endoplasmic
reticulum (while it remains in the chrysalis), that likely
form cubic membranes, folded according to the form of the Gyroid. The subsequent formation of the chiral hard chitin framework
is suggested to be driven by the gradual polymerisation of the chitin
precursors, whose inherent chiral assembly in solution (during
growth) promotes the formation of a single enantiomer.
 Stephen T. Hyde and Olaf Delgado Friedrichs, “From untangled nets to tangled materials”, Solid State Sci., in press (2010). DOI 10.1016/j.solidstatesciences.2010.10.028
pdf
version (1.1 MB)
Abstract:
We suggest constructive deﬁnitions for the determination of untangled ﬁnite graphs and threeperiodic
nets, using barycentric embeddings in two and three dimensions. The possibility of deliberately con
structing tangled graphs and nets is canvassed, and we conclude that tangled patterns offer a novel class
of nano and mesostructured materials with useful features, including high internal surface area and
volume and chirality.
 Liliana de Campo, Trond Varslot, Minoo J. Moghaddam, Jacob J. K. Kirkensgaard, Kell Mortensen and Stephen T. Hyde, “A
Novel Lyotropic Liquid Crystal Formed by Triphilic StarPolyphiles:
Hydrophilic/Oleophilic/Fluorophilic Rods Arranged in a 12.6.4. tiling”, Phys Chem Chem Phys, DOI:10.1039/C0CP01201G (2010).
pdf
version (2.4 MB)
Abstract:
Triphilic starpolyphiles are shortchain oligomeric molecules with a radial arrangement of
hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number
of liquid crystalline structures when mixed with water. In this contribution we focus on a
hexagonal liquid crystalline mesophase found in starpolyphiles as compared to the corresponding
double chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact
demixed in these starpolyphile systems, or whether both hydrocarbon and fluorocarbon chains are
miscible, leading to a single hydrophobic domain, making the starpolyphile effectively
amphiphilic. We report SANS contrast variation data that is compatible only with the presence of
three distinct immiscible domains within this hexagonal mesophase, confirming that these star
polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3phase systems.
Quantitative comparison with scattering simulations shows that the experimental data are in very
good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic
hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains)
are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic
domains and fluorophilic quadrangular prismatic domains.
 Stephen T. Hyde, “Contemporary geometry for the built design?”, Architecture Theory Review, 15(2), 210, (2010).
pdf
version (2.3 MB)
+erratum
Abstract:
I explore the terrain that lies
between architecture and geometry, from the perspective of a structural
scientist with no professional architectural expertise. The divide
between these disciplines perhaps stems from an ancient dichotomy
between the art vs. engineering schools of architecture, fertilised by
the current dogma that art and science can never meet. Architects stand
to gain much from study of the spectacular advances in geometry in
recent decades, such as the growing understanding of cellular patterns
in space, tiles, nets and curved surfaces. Some examples of those
advances are discussed in detail. I conclude that both architecture and
geometry would beneﬁt from a renewed mutual interest.
 T. Castle, Myfanwy E. Evans and S. T. Hyde, “All toroidal
embeddings of polyhedral graphs in 3space are chiral”, New J. Chem.,
2009, 33, 2107  2113 (2009).
pdf
version (1.3 MB)
Abstract:
We investigate the possibility of forming achiral knottings of polyhedral (3connected) graphs
whose minimal embeddings lie in the genusone torus. Various analyses to show that all examples
are chiral. This result suggests a simple route to forming chiral molecules via templating on a
toroidal substrate.
 Stephen T. Hyde, Liliana de Campo and Christophe Oguey,
“Tricontinuous mesophases of balanced threearm ‘star polyphiles’ " , Soft
Matter, 5, 2782–2794, (2009). DOI: 10.1039/b822814k
pdf
version (11.1 MB)
Abstract:
We construct simple models to compare ordered tricontinuous patterns that are topologically
consistent with the constraints imposed by threearm star polyphile selfassembly, analogous to steric
packing and elastic bending models used to analyse bicontinuous mesophases in amphiphilic
assemblies. We ﬁnd a number of competing lowenergy ordered structures, composed of threading of
three identical labyrinths, with threefold inﬁnite branch lines, that are likely to be of comparable
energy for polyphile shapes with moderately splayed arms. These patterns are triplyperiodic analogues
of the hexagonal honeycomb, which is most favoured for unsplayed threearm polyphile architectures.
 Jacob Judas Kain Kirkensgaard and Stephen T. Hyde, “Beyond
amphiphiles: Coarsegrained simulations of starpolyphile liquid
crystalline assemblies”, Phys. Chem. Chem. Phys., 11, 2016  2022,
(2009).
pdf
version (1.5 MB)
Abstract:
We have simulated the selfassembly of a novel class of threearm molecules,
ABC stararchitecture polyphiles, using coarsegrained bead simulations. A number of
topologically complex liquid crystalline mesostructures arise that can be related to the
betterknown bicontinuous mesophases of lyotropic amphiphilic systems. The simulations reveal
3D selfassemblies whose structural variations follow those expected assuming a simple steric
molecular packing model as a function of star polyphile splay and relative volumes of each arm
in the polyphile. The splay of each arm, characterised by the 3D wedgeshape emanating from the
core of each molecule to its exterior induces torsion of the interfaces along the triple lines,
whereas differences in the relative volumes of arms induce curvature of the triple lines. Three
distinct mesostructures are described, characterised by their microdomain topologies, which are
unknown in simpler amphiphilic systems, but resemble in some respects bicontinuous mesophases.
These three (or more) arm polyphilic systems offer an interesting extension to the betterknown
selfassembly of (twoarm) amphiphiles in solution.
Abstract:
Precipitation of barium or strontium carbonates in alkaline silicarich
environments leads to crystalline aggregates that have been named
silica/carbonate
biomorphs because they resemble the morphology of
primitive organisms. These
aggregates are selfassembled materials of
purely inorganic origin, with an amorphous
phase of silica intimately
intertwined with a carbonate nanocrystalline phase. We
propose a
mechanism that explains all the morphologies described for biomorphs.
Chemically coupled coprecipitation of carbonate and silica leads to
fibrillation
of the growing front and to laminar structures that experience
curling on their
growing rim. These curls propagate surflike along the rim
of the laminae. Observed
morphologies with smoothly varying curvatures
can be explained by the combined growth of
counterpropagating curls
and growing laminae.
Comments on this paper can be found at:
 Matthias Kellermeier, Fabian Glaab, Anna M. Carnerup, Markus
Drechsler, Benjamin Gossler, Stephen T. Hyde, and Werner Kunz,
“Additiveinduced
morphological tuning of selfassembled silicabarium
carbonate crystal aggregates” , J Cryst Growth, 311, 25302541, doi:10....sgro.2009.02.044, (2009).
Abstract:
Crystallisation of barium carbonate from alkaline silica
solutions results in the
formation of extraordinary micronscale
architectures exhibiting
noncrystallographic curved shapes, such as
helical filaments and wormlike braids.
These socalled “silica
biomorphs” consist of a textured assembly of uniform
elongated
witherite nanocrystallites, which is occasionally sheathed by a skin of
amorphous silica. Although great efforts have been devoted to
clarifying the
physical origin of these fascinating materials, to date
little is known about the
processes underlying the observed
selforganisation. Herein, we describe the effect
of two selected
additives, a cationic surfactant and a cationic polymer, on the
morphology of the forming crystal aggregates, and relate changes to
experiments
conducted in the absence of additives. Minor amounts of
both substances are shown
to exert a significant influence on the
growth process, leading to the formation of
predominantly flowerlike
spherulitic aggregates. The observed effects are discussed
in terms of
feasible morphogenesis pathways. Based on the assumption of a
template
membrane steering biomorph formation, it is proposed that the two
additives are capable of performing specific bridging functions
promoting the
aggregation of colloidal silica which constitutes the
membrane. Morphological
changes are tentatively ascribed to varying
colloid coordination effecting distinct
membrane curvatures.
 S.J. Ramsden, V. Robins and Stephen Hyde, "3D euclidean nets from
2D hyperbolic tilings: Kaleidoscopic examples", Acta
Crystallogr. A,
A65, 81108 (2009) [Lead Article.]
Abstract:
We present a method for geometric construction of periodic
3D Euclidean nets by
projecting 2D hyperbolic tilings onto a family of triply
periodic minimal surfaces (TPMS).
Our techniques extend the combinatorial tiling theory of Dress, Huson,
and
DelgadoFriedrichs to enumerate simple reticulations of
these TPMS.
We include a taxonomy of all networks arising from
kaleidoscopic hyperbolic
tilings with up to two distinct tile types (and dually two
vertex types), mapped
to three related TPMS, namely Schwarz's Primitive (P) and
Diamond (D) surfaces,
and Schoen's Gyroid (G)
 Stephen T. Hyde, Michael O’Keeffe and Davide M. Proserpio, "A short history of an elusive yet
ubiquitous structure in chemistry, materials and mathematics",
Angew. Chemie Int. Ed., 47, 79968000 (2008).
http://dx.doi.org/10.1002/anie.200801519
Abstract:
Herein we describe some
properties and the occurrences of a beautiful geometric
figure that is ubiquitous in chemistry and materials science, however,
it is not as
wellknown as it should be. We call attention to the need for
mathematicians to pay
more attention to the richly structured natural world, and for
materials scientists to
learn a little more about mathematics. Our account is informal and
eschews any
pretence of mathematical rigor, but does start with some necessary
mathematics.
 Toen Castle, Myfanwy E. Evans and S.T Hyde, “Ravels: Knotfree but not free.
Novel entanglements of graphs in 3space”, New J Chem, 32,
14841492 (2008).
doi:10.1039/b719665b
Abstract:
Molecular and extended framework
materials, from proteins to catenanes and metal–organic
frameworks, can assume knotted conﬁgurations in their bonding
networks (the chemical graph).
Indeed, knot theory and structural chemistry have remained closely
allied, due to those
connections. Here we introduce a new class of graph entanglement:
‘‘ravels’’. These ravels—often
chiral—tangle a graph without the presence of knots. Just as knots lie
within cycles in the graph,
ravels lie in the vicinity of a vertex. We introduce various species of
ravels, including fragile
ravels, composite ravels and shelled ravels. The role of ravels is
examined in the context of ﬁnite
and inﬁnite graphs—analogous to molecular and extended
framework nets—related to the
diamond net.

Zakaria
A. Almsherqi, Stephen T. Hyde, Malarmathy Ramachandran, Yuru Deng, “Cubic membranes: a structurebased
design for DNA uptake”, J. R. Soc. Interface, 5, 10231029
(2008).
doi:10.1098/rsif.2007.1351
Abstract:
Cubic membranes are soft
threedimensional crystals found within cell organelles in a variety
of living systems, despite the aphorism of Fedorov: ‘crystallization is
death’. They consist of
multibilayer lipid–protein stacks, folded onto anticlastic surfaces
that resemble triply
periodic minimal surfaces, forming highly swollen crystalline sponges.
Although cubic
membranes have been observed in numerous cell types and under different
pathophysiolo
gical conditions, knowledge about the formation and potential
function(s) of nonlamellar,
cubic structures in biological systems is scarce. We report that
mitochondria with this cubic
membrane organization isolated from starved amoeba Chaos carolinense
interact sufﬁciently
with short segments of phosphorothioate oligonucleotides ( PSODNs) to
give signiﬁcant
ODNs uptake. ODNs condensed within the convoluted channels of cubic
membrane by an
unknown passive targeting mechanism. Moreover, the interaction between
ODNs and cubic
membrane is sufﬁcient to retard electrophoretic mobility of
the ODN component in the gel
matrix. These ODN–cubic membrane complexes are readily internalized
within the
cytoplasm of cultured mammalian cells. Transmission electron
microscopic analysis conﬁrms
ODNs uptake by cubic membranes and internalization of ODN–cubic
membrane complexes
into the culture cells. Cubic membranes thus may offer a new,
potentially benign medium for
gene transfection.
 Alina E. Voinescu, Matthias Kellermeier, Anna M. Carnerup,
AnnKristin Larsson, Didier Touraud, Werner Kunz, Lorenz Kienle, Arno
Pfitzner and Stephen T. Hyde and, “Inorganic Selforganized silica
aragonite biomorphic composites”, Cryst Growth Design, 8,
15151521 (2008).
Abstract:
The precipitation of calcium
carbonate in alkaline silica solutions results in the formation of
complex curvilinear
forms if aragonite formation is encouraged by growth at an elevated
temperature (80 °C). The resulting coralline selfassembled
silicacalcium carbonate particles are “biomorphs”, bearing
a striking resemblance to natural coral forms. These materials,
comprised
of calcium carbonate nanocrystals and an amorphous silica matrix, have
a complex ultrastructure, made of clusters of gathered
sheets of variable curvatures formed by successive curling. The
nanocrystals within these “ruled surfaces” are thin,
elongated,
densely packed needles of aragonite. These clusters are outgrowths from
central saddlelike cores that resemble developable petaloid
surfaces. The size, shape, crystallography, and chemical composition of
the resulting biomorphs were examined by optical microscopy,
ﬁeld emission scanning electron microscopy (FESEM), powder
Xray
diffractometry (XRD), Fourier transform infrared spectroscopy
(FTIR), transmission electron microscopy (TEM and HRTEM), and energy
dispersive Xray analysis (EDX).
 G.E. SchröderTurk, A. Fogden and S.T.Hyde, ” Local
v/a variations as a measure of structural packing frustration in
bicontinuous mesophases, and geometric arguments for an alternating
Im3m (IWP) phase in blockcopolymers with polydispersity”, Eur.
Phys. J., B59, 115126 (2007).
Abstract:
This article explores global
geometric features of bicontinuous spacepartitions and their rele
vance to selfassembly of blockcopolymers. Using a robust
deﬁnition of ‘local channel radius’, based on the
concept of a medial surface [1], we relate radius variations of the
spacepartition to polymolecular chain
stretching in bicontinuous diblock and terblock copolymer assemblies.
We associate local surface patches
with corresponding cellular volume elements, to deﬁne local
volumetosurface ratios. The distribution of
these v/a ratios and of the channel radii are used to quantify the
degree of packing frustration of molecular
chains as a function of the speciﬁc bicontinuous geometry,
modelled by triplyperiodic minimal surfaces
and related parallel interfaces. The Gyroid geometry emerges as the
most nearly homogeneous bicontinu
ous form, with the smallest heterogeneity of channel radii, compared to
the cubic Primitive and Diamond
surfaces. We clarify a geometric feature of the Gyroid geometry: the
threecoordinated nodes of the graph
are not the widest points of the labyrinths; the widest points are at
the midpoints of the edges. We also ex
plore a more complex cubic triplyperiodic surface, the IWP surface,
containing two geometrically distinct
channel subdomains. One of the two channel systems is nearly as
homogeneous in local channel diameters
as the Gyroid, the other is more heterogeneous than the Primitive
surface. Its hybrid nature suggests the
possibility of an “alternating IWP” phase in polydisperse linear
ABCterpolymer blends, with monodis
perse molecular weight distributions (MWD) in the A and B blocks and a
more polydisperse C block.
 Alina E. Voinescu, Matthias Kellermeier, Anna M. Carnerup,
AnnKristin Larsson, Didier Touraud, Stephen T. Hyde and W. Kunz,
“Coprecipitation of silica
and alkalineearth carbonates using TEOS as silica source”, J
Cryst Growth, 306 152158 (2007).
Abstract:
We explore the use of
tetraethoxysilane (TEOS) as a silica source for the formation of
carbonatesilica composite materials known as ‘biomorphs’. The basic
hydrolysis of
TEOS furnishes silica in a controllable fashion, allowing a
signiﬁcantly higher reproducibility
of the obtained silica–barium and silica–strontium carbonate
coprecipitates compared to
commercial water glass silica used so far. We further discuss the
inﬂuence of ethanol used
as a cosolvent on the morphologies of biomorphs, which are examined by
optical microscopy,
ﬁeld emission scanning electron microscopy (FESEM) and energy
dispersive Xray analysis (EDX).
 S.T. Hyde and G.E. SchröderTurk, “Tangled (up in) Cubes”, Acta
Cryst A63 186197 (2007).
Abstract:
The ‘simplest’ entanglements of
the graph of edges of the cube are enumerated,
forming twocell {6, 3} (hexagonal mesh) complexes on the genusone
two
dimensional torus. Five chiral pairs of knotted graphs are found. The
examples
contain nontrivial knotted and/or linked subgraphs [(2, 2), (2, 4)
torus links and
(3, 2), (4, 3) torus knots].
 G.E. Schröder, A. Fogden and S.T. Hyde, “Bicontinuous
geometries and molecular selfassembly: Comparison of local curvature
and global packing variation in genusthree cubic, tetragonal and
rhombohedral surfaces”, Eur Phys J B, 54 509524 (2006).
Abstract:
Balanced inﬁnite
periodic minimal surface families that contain the cubic Gyroid (G),
Diamond
(D) and Primitive (P) surfaces are studied in terms of their global
packing and local curvature properties.
These properties are central to understanding the formation of
mesophases in amphiphile and copolymer
molecular systems. The surfaces investigated are the tetragonal,
rhombohedral and hexagonal tD, tP, tG,
rG, rPD and H surfaces. These noncubic minimal surfaces furnish
topologypreserving transformation
pathways between the three cubic surfaces. We introduce ‘packing (or
global) homogeneity’, deﬁned as
the standard deviation ∆d of the distribution of the channel diameter
throughout the labyrinth, where
the channel diameter d is determined from the medial surface skeleton
centered within the labyrinthine
domains. Curvature homogeneity is deﬁned similarly as the
standard deviation ∆K of the distribution of
Gaussian curvature. All data are presented for distinct length
normalisations: constant surfacetovolume
ratio, constant average Gaussian curvature and constant average channel
diameter. We provide ﬁrst and
second moments of the distribution of channel diameter for all members
of these surfaces complementing
curvature data from [A. Fogden, S. Hyde, Eur. Phys. J. B 7, 91 (1999)].
The cubic G and D surfaces
are deep local minima of ∆d along the surface families (with G more
homogeneous than D), whereas the
cubic P surface is an inﬂection point of ∆d with adjacent,
more homogeneous surface members. Both
curvature and packing homogeneity favour the tetragonal route between G
and D (via tG and tD surfaces)
in preference to the rhombohedral route (via rG and rPD).
 S.T. Hyde, O. Delgado Friedrichs, S.J. Ramsden and V.
Robins, “Towards enumeration
of crystalline frameworks: the 2D hyperbolic approach”, Solid
State Sciences 8 740752 (2006).
pdf
version (1.1 MB)
Abstract:
Crystalline frameworks in 3D
Euclidean space can be constructed by projecting tilings
of 2D hyperbolic space onto threeperiodic minimal surfaces, giving
surface reticulations.
The technique involves Delaney–Dress tiling theory, group theory,
differential and
nonEuclidean geometry. Preliminary results of this approach, found at
http://epinet.anu.edu.au, are discussed and compared with other
approaches.
 V. Robins, S.J. Ramsden and S.T. Hyde, “A note on the two
symmetrypreserving covering maps of the Gyroid minimal surface”,
Eur Phys J B 48 107111 (2005).
pdf
version (276 kB)
Abstract:
Our study of the gyroid minimal
surface has revealed that there are two distinct covering
maps from the hyperbolic plane onto the surface that respect its
intrinsic symmetries.
We show that if a decoration of H2 is chiral, the pro jection of this
pattern via the two
covering maps gives rise to distinct structures in E3 .
 T. Aste, T. Di Matteo and S.T. Hyde, "Complex networks on hyperbolic
surfaces", Physica A, 346, pp. 2026 (2005).
[Also available at LANL
arXiv]

pdf
version (308 kB)
Abstract:
We
explore a novel method to generate and characterize complex
networks by means of
their
embedding on hyperbolic surfaces. Evolution through local
elementary moves allows the
exploration
of the ensemble of networks which share common
embeddings and consequently
share
similar hierarchical properties. This method provides a new
perspective to classify
networkcomplexity
both on local and global scale. We demonstrate
by means of several
examples
that there is a strong relation between the network
properties and the embedding
surface.
 T. Di Matteo, T. Aste, S. T. Hyde and S. Ramsden, "Interest rates hierarchical
structure", Physica A, A355, 2133 (2005)

pdf
preprint (560 KB)
Abstract:
We
propose a general method to study the hierarchical
organization of financial data.
The
statistical, geometrical and topological properties of
such data are analyzed by
embedding
the structure of their correlations in metric
graphs in multidimensional spaces.
We
show an application to two different sets of
interest rates data. In this case we
construct
triangular embeddings on the sphere. The resulting graph contains the
minimum
spanning tree as subgraph and it preserves
its hierarchical structure.
This results
in
a clear cluster differentiation and allows
to compute new local and global topological
quantities.
A three dimensional
representation of this embedding is constructed together
with
its projection on a plane by
using the Pelting method and a relaxation procedure to
converge
on the correct
metric geometry.
 A. V. Rode, E. G. Gamaly, A. G. Christy, J. G. Fitz Gerald, S.
T. Hyde, R. G. Elliman, B. LutherDavies, A. I. Veinger, J.
Androulakis, J. Giapintzakis, "Unconventional
magnetism in allcarbon nanofoam", Phys Rev B 70,
054407 (2004). DOI: 10.1103/PhysRevB.70.054407
[Also
available at
LANL archive].

pdf version
(500 KB)
Abstract:
We
report production of nanostructured magnetic carbon
foam by a highrepetitionrate,
highpower
lase ablation of glassy carbon in Ar atmosphere. A
combination
of
characterization
techniques revealed that the system contains both sp2
and sp3 bonded
carbon
atoms. The
material is a form of carbon containing graphitelike sheets
with
hyperbolic
curvature, as proposed for
"schwarzite." The foam exhibits ferromagneticlike
behavior
up to 90 K, with a narrow hysteresis curve and a
high saturation magnetization.
Such
magneticproperties are very unusual for a carbon
allotrope.
Detailed analysis
excludes
impurities as the origin of themagnetic signal. We
postulate that localized
unpaired
spins occur because of topological and bonding defects
associated with the
sheet
curvature, and that these spins
are stabilized due to the steric protection offered
by
the convoluted sheets.
 T. Di Matteo, T. Aste and S.T. Hyde, "Exchanges in complex networks:
income and wealth" in The Physics of
Complex Systems (New advances and Perspectives) edited by F. Mallamace
and H. E. Stanley, Proceedings of the International School of Physics
"Enrico Fermi", (IOS Press, Amsterdam 2004) p. 435442 (also available from the LANL arXiv )

pdf
version (1.5 MB)
Abstract:
We
investigate the wealth evolution in a
system of agents that ex
change
wealth through a disordered network in presence of an
additive stochastic
Gaussian
noise. We show that the resulting wealth distribution is
shaped by the de
gree
distribution of the underlying network and in particular we
verify that scale free
networks
generate distributions with powerlaw tails in the
highincome region. Nu
merical
simulations of wealth exchanges performed on two different
kind of networks
show
the inner relation between the wealth distribution and the
network properties
and
confirm the agreement with a selfconsistent solution. We show
that empirical
data
for the income distribution in Australia are qualitatively
well described by our
theoretical
predictions.
 Vanessa Robins, Stuart Ramsden and Stephen Hyde, "2D hyperbolic groups induce
3periodic euclidean reticulations", European Physical
Journal B, 39, pp. 365375 (2004). DOI: 10,1140/epjb/e2004002022

pdf
version (1.2 MB)
Abstract:
Many
crystalline networks can be viewed as
decorations of triply periodic minimal surfaces.
Such
surfaces are covered by the hyperbolic plane, in the same way
that the euclidean
plane
covers a cylinder. Thus, a symmetric hyperbolic network can
be wrapped onto an
appropriate
minimal surface to obtain a 3d periodic net. This
requires symmetries of the
hyperbolic
net to match the symmetries of the minimal surface. We
describe a systematic
algorithm
to find all the hyperbolic symmetries that are
commensurate with a given
minimal
surface, and the generation of simple 3d nets from these
symmetry groups.
 Stephen T. Hyde, Anna M. Carnerup, AnnKristin Larsson and
Andrew G. Christy, "Selfassembly
of carbonatesilica colloids: between living and nonliving form",
Physica, 339, pp, 2433, (2004).

pdf
version (500 KB)
Abstract:
We
describe selfassembled
silicacarbonate aggregates that show a diverse range of
morphologies,
all of which display complex internal structure,
orientational ordering
of
components, and wellorganised, curved global morphologies that
bear a strong
resemblance
to biogenic forms. The internal order is described as
a liquidcrystallike
organisation
of colloidal particles. We discuss possible causes
for the striking
morphologies
of these inorganic materials, including local
nanocrystal packing constraints
and
global silica membrane templating.
 G.E. Schröder, S.J. Ramsden, A. Fogden and S.T. Hyde, "A rhombohedral family of minimal
surfaces as a pathway between the P and D cubic mesophases", Physica
A, 339, pp. 137144, (2004).

pdf
version (350 KB)
Abstract:
This
article presents a medial surface
analysis of the rhombohedral infinite periodic
minimal
surface rPD. This oneparameter family of
labyrinthforming, bicontinuous
surfaces
has been suggested as a continuous pathway for
transitions between its
two
cubic members, the Primitive and the Diamond surface, e.g. in
mesophases in
liquidcrystalline
selfassembly processes. By providing a
definition of a pointwise
channel
diameter, the MS allows for the analysis of packing
properties, stretching
frustration
and homogeneity of such surfaces that cannot be
deduced from curvature
characteristics
alone. The medial surface (MS) is a representation
of a labyrinth
structure
as an embedded and centered 2D skeleton, and is a
geometrically equivalent
description
of the labyrinth as the labyrinth itself. It can be
further reduced to a
welldefined
1D line graph. For the rPD surface, we show that
variations of the channel
diameter
are locally minimal for the member corresponding to the D
surface,
and
a horizontal inflection point in the case of the P surface.
This may have implications
for
the phase stability of corresponding liquidcrystalline
mesophases. We also
demonstrate
that a 1D line graph, if geometrically centered within
the labyrinth,
contains
curved edges and cannot be deduced from symmetry
considerations alone.
 Maurizio Olla, Armin Semmler, Maura Monduzzi and Stephen T.
Hyde, "From Monolayers to
Bilayers: Mesostructural Evolution in DDAB/water/tetradecane
microemulsions", Journal of Physical Chemistry B, 108,
pp. 1283312841, (2004). DOI: 10.102 1/jp03796 1v.

pdf
version (340 KB)
Abstract:
Small
angle xray (SAXS) scattering and 14N NMR relaxation were
determined
for microemulsion samples formed from didodecyl dimethyl
ammonium
bromide (DDAB), water and tetradecane to deduce the
associated
microstructures.
The swelling features within the
tetradecane
microemulsion
are unusual compared with DDAB/water/alkane
analogs formed
with
shorter nalkanes: tetradecanecontaining
microemulsions do not show the
characteristic
antipercolation
transition seen for the latter microemulsions.
Experimental
data
along tetradecane dilution lines are consistent with a
continuous
transition from a bilayer to monolayer structure of the surfactant
interface.
The
evolution is topologically complex. It involves the
annealing of bilayer punctures
that
occur on oil dilution. A
quantitative model that allows continuous transformation
from
multihandled bilayers (typical of L3 sponge mesophases) to
multihandled
monolayers
(typical of microemulsions modelled with
shorter chained alkanes)
is
proposed that fits well the observed
behaviour.
 S.T. Hyde and J.M. García Ruiz, "Complex materials from simple
chemistry: biomorphs and biomaterials", L'Actualité
Chimique, no. 275, mai, pp. 406 (2004).

pdf version (336 KB)
Abstract:
A
variety of lifelike "biomorphs" can be grown by
coprecipitation of silica
and
alkalineearth carbonates at high pH. Forms include twisted
filaments
and
sheets, that are indistinguishable from microscopic inclusions
in
ancient
rocks, commonly identified as ancient microfossils.
Biomorphs are
spectacular
examples of selfassembled inorganic colloids, forming
composites
of nmsized rodshaped carbonate nanocrystals and
colloidal
amorphous
silica spheres. The structural complexity of these
materials, with
orientational
and translational order/disorder at distinct length
scales, is
reminiscent
of many hard biomaterials, such as bone.
 Eugenie C. Scott[*], Nicholas J. Matzke[*], Glenn
Branch[*], Stephen T. Abedon[S][$],Stephen Addison[S] Stephen L.
Adler[S] Stephen B. Aley[S] Stephen C. Alley[S] Steven I. Altschuler[S]
Stephen Robert Anderson[S] Stephen W. Arch[S] J. Steven Arnold[S]
Stevan J. Arnold[S] Steven N. Austad[S] Stephen Azevedo[S] Stephen
Charles Bain[S] Stephen M. Baird[S] Steven A. Balbus[S] Steven W.
Barger[S] Stephen John Barnett[S] Stephen Barrett[S] Steven J.
Baskauf[S] Stephen Joseph Richard Battersby[S] Steven C. Beadle[S]
Steven K. Beckendorf[S] Stephen Beckerman[S] Steven R. Beissinger[S]
Steven M. Bellovin[S] Stephanie J. Belovich[S] Steve G. Belovich[S]
Stephen P. Bentivenga[S] Steven Bergman[S] Steven Bart Bertman[S]
Stephen Blackmore[S] Steven M. Block[S] Steven Bodovitz[S] Stephen A.
Boffey[S] Stephen Patrick Bonser[S] Stephen H. Bowen[S] Stephen
Bowlus[S] Steven G. Boxer[S] Steven E. Brenner[S] Steven D. Brewer[S]
Stephen Brick[S] Steven Briggs[S] Steven Brill[S] Stephen Brown[S]
Stephen Brown[S][!], Stephen L. Brown[S] Stephen R. Brown[S] Steven W.
Brown[S] Steven B. Broyles[S] Stephen G. Brush[S] Stephen H. Bryant[S]
Stephen Burke[S] Stephen Burnett[S] Stephen J. Burns[S] Stephen D.
Busack[S] Steven W. Buskirk[S] Steve Butcher[S] Steven N. Byers[S]
Stephen D. Cairns[S] Stephen Cameron[S] Steven K. Campbell[S] Steven
Carlip[S] Stephen R. Carpenter[S] Steven A. Carr[S] Steven M. Carr[S]
Steve Carroll[S] Steven B. Carroll[S] Steven B. Case[S] Steven L.
Chown[S] Steven Chu[S][N], Steven E. Churchill[S] Steven Gerard
Clarke[S] Steven Earl Clemants[S] Steven C. Clemens[S] Steven S.
Cliff[S] Steven J. Collins[S] Steven C. Corbato[S] Steve Cox[S] Stephen
H. Crandall[S] Stephen T. Crews[S] Steve Croft[S] Stephan G. Custer[S]
Steven D'Hondt[S] J. Steven de Belle[S] Stephen M. Deban[S] Stephen J.
DeCanio[S] Stephen B. Deitz[S] Steven J. DeMarco[S] Steven R.
DePalma[S] Stephen H. Devoto[S] Steven P. Dettwyler[S] Stephen
Dewhurst[S] Steve Dickman[S] Stephen P. DiFazio[S] Steven H. Dillman[S]
Stephen G. DiMagno[S] Steve DiNardo[S] Stephen S. Ditchkoff[S] Stephen
Kenneth Donovan[S] Stephen Q. Dornbos[S] Stephen M. Downes[S] Steven M.
Drucker[S] Stephen A. Drury[S] Steven R. Dudgeon[S] Steven R. Dunn[S]
Steven I. Dutch[S] Steven Eiger[S] Stephen T. Elbert[S] Stephen P.
Ellner[S] Stefan Estreicher[S] Steven Neil Evans[S] Stephen E.
Feinberg[S] Steven L. Forman[S] Steve Fornaca[S] Steven Freedberg[S]
Stephen Freeland[S] Stephen R. Frost[S] Stephanie M. Fullerton[S] Steve
Gaines[S] Stephen C. Gammie[S] Steven W. Gangestad[S] J. Stephen
Gantt[S] Steven Garrett[S] Steve Gaulin[S] Stephen M. Gentleman[S]
Stephen A. George[S] Steven F. Gessert[S] Stephen R. Getty[S] Steven R.
Gill[S] Stephen Giovannoni[S] Stephen P. Goff[S] Steven F. Goldberg[S]
Stephen D. Goldinger[S] Stephen W. Golladay[S] Steven C. Good[S]
Stephen Bruce Goodwin[S] Stephen R. Graham[S] Stephen Grand[S] Steven
Green[S] Steven Green[S][!], Stephen Gregory[S] Stephen Grill[S]
Stephen W. Grimes[S] Steven P. Gross[S] Steve Guggenheim[S] Steven R.
Gullans[S] Stephen B. Haber[S] Steven J. Hageman[S] Stephen B. Hager[S]
Stephen J. Haggarty[S] Stephen R. Hahn[S] Steven E. Hall[S] Steve
Halperin[S] Steven W. Hamilton[S] Stephen K. Hamilton[S] Steven C.
Hand[S] Steven N. Handel[S] Stephen Hanzély[S] Stephen C.
Harrison[S], Stephen D. Harrison[S], Steve E. Hartman[S], Stephen C.
Harvey[S], Stephen T. Hasiotis[S], Stephen D. Hauschka[S], Stephen W.
Hawking[S][%], Stephen C. Hawkins[S], Stephen B. Heard[S], Stephen M.
Hedrick[S], Steven James Heggie[S], Stephen Henderson[S], Steve
Henikoff[S], Stephen Henley[S], Steven J. Hoekstra[S], Steven L.
Hopp[S], Stephane Marc Hourdez[S], Steven A. Hovan[S], R. Stephen
Howard[S], Stephen P. Hubbell[S], Steve E. Humphries[S], Stephen C.
Hurlock[S], Steve Huskey[S], Stephen T. Hyde[S], Steven Q. Irvine[S], Steven H. Izen[S], Steven Erik
Jacobsen[S], Steven Robert Jayne[S], Steve Jeffery[S], Stephen H.
Jenkins[S], Steven L. Jensen[S], Steven L. Jessup[S], Stephen D.
Jett[S], Steve Jones[S], Steve Josephson[S], Steven A. Juliano[S],
Stephen M. Kajiura[S], Steve Kane[S], Stephen A. Karl[S], Steve
Karr[S], Stephen J. Kaufman[S], Stephen B. H. Kent[S], Stephen Kent[S],
Stephen J. King[S], Steve King[S], Stephen T. Kinsey[S], Steven L.
Kipp[S], Stefan Koenemann[S], Steven E. Koonin[S], Stephen
Kowalczykowski[S], Stephen A. Kowalewski[S], Stephen J. Kron[S], Steven
L. Kuhn[S], Stephen G. LaBonne[S], Stephen Laurence[S], Stephen E. G.
Lea[S], Steven Bruce Legg[S], Steven L. Lehman[S], Stephen H.
Lekson[S], Stephan A. Leslie[S], Stephen D. Levene[S], Steven P.
Lewis[S], Steven L. Lima[S], Stefan G. Llewellyn Smith[S], J. Stephen
Lodmell[S], Steven T. LoDuca[S], Stephen H. Loomis[S], Stephen C.
Luce[S], Steven J. Luck[S], Stephen Andrew Lunn[S], Stefan Luschnig[S],
Steven Raymond Lustig[S], Steven P. Lynch[S], Stephen P. Mackessy[S],
Stephen Maddock[S], Stephanie Lee Madson[S], Steven Main[S], Stephen B.
Malcolm[S], Stephen M. Marek[S], Stephanie Marin[S], Steven Mathews[S],
Stephan Matthiesen[S], Steve Matzner[S], Steven S. Maughan[S], Stephen
J. Maxfield[S], Stephanie Mayer[S], Steven McCommas[S], Steven P.
McConnell[S], Steven McCullagh[S], Stephen M. McDuffie[S], Stephen T.
McGarvey[S], Stephen A. Miller[S], Stephen M. Miller[S], Stephen J.
Mojzsis[S], Stephen Mondy[S], Stephen Monismith[S], Steve Morris[S],
Stephen A. Morse[S], Steve Moulton[S], Stephen M. Mount[S], Esteban
Muldavin[S], Stephen S. Mulkey[S], Stephen J. Mullin[S], Stephen H.
Munroe[S], Steven Murov[S], Steven F. Myers[S], Steven T. Myers[S],
Steven A. Nadler[S], Steve Nahn[S], Steven L. Neuberg[S], Stephen
Norley[S], Steven P. Novella[S], Stephen Nowicki[S], Stephen J.
O'Brien[S], Steven Wayne O'Neal[S], Steven Orzack[S], Stephen
Ousley[S], Steve Paddock[S], Stephen R. Palumbi[S], Stephen Park[S],
Stephen M. Pasquale[S], Steven L. Peck[S], Steve Pells[S], Stephen W.
Pierson[S], Steven Pinker[S], Steven PirieShepherd[S], Steven M.
Platek[S], Steven Samuel Plotkin[S], Stephen Pollaine[S], Steven E.
Poltrock[S], Steve M. Potter[S], Steven J. Projan[S], Stephen James
Prowse[S], Stephen PruettJones[S], Stephen Quake[S], Steven
Radosevich[S], Stefan Rahmstorf[S], Steve Reid[S], Steve Renals[S],
Stephen M. Rich[S], Stephen M. Richard[S], Stephen Richards[S], Stephen
Giles Richardson[S], Steve Rissing[S], Stephen John Roberts[S], Stephen
P. Roberts[S], Stephen Robertson[S], Steven Robinow[S], Steven M.
Roels[S], Steven H. Rogstad[S], Steve Roof[S], Stephen A. Rose[S],
Steven Rose[S], Stephen Roser[S], Stephen T. Ross[S], Stephen M.
Roth[S], Stephen Rothman[S], Stephen I. Rothstein[S], Steve
Rounsley[S], Stephen M. Rowland[S], Steve Rowley[S], Steven W.
Runge[S], Steve Salisbury[S], Steven L. Salzberg[S], Steve Saunders[S],
Stephen G. Saupe[S], Stephen W. Schaeffer[S], Steven D. Schafersman[S],
Stephen F. Schaffner[S], Steven Jay Scheinman[S], Steven J. Scher[S],
Steven M. Schildcrout[S], Stephen E. Schneider[S], Stephen H.
Schneider[S], Stephan Q. Schneider[S], Stefan Schnitzer[S], Stephan J.
Schoech[S], Steven M. Schrader[S], Stephan Schulz[S], Stephen R.
Schutter[S], Stephen M. Schwartz[S], Steve Schwartz[S], Steve
Scofield[S], Stephen L. Scott[S], Steven Seavey[S], Steven Selden[S],
Stephen J. Seligman[S], Steven Semken[S], Steven Shackley[S], Stephen
J. Shawl[S], Steve Sheffield[S], Stephen Shennan[S], Steven
Sherwood[S], Stephen B. Shope[S], Stephen M. Shuster[S], Steven
Siciliano[S], Stephen C. Sillett[S], Stephen J. Simpson[S], Stephen T.
Smale[S], Stephen J. Smith[S], Steve E. Smith[S], Steven Thomas
Smith[S], Stefan Sommer[S], Stephanie Rena Songer[S], Steven Peter
Souza[S], Stephen Spiro[S], Stephen Sprang[S], Stephen M. Stack[S],
Stephen D. Stahl[S], Stephen E. Stancyk[S], Steven M. Stanley[S],
Stephen C. Stearns[S], Stephen P. Stich[S], Steve Stowers[S], Stefan
Strack[S], Steve Strand[S], Steve Strassmann[S], Steve Strauss[S],
Stephen A. Stricker[S], Steven A. Sullivan[S], Steven M. Taffet[S],
Stephen J. Tapscott[S], Steve Taylor[S], Stephen Harrold Tedder[S],
Stephen Temperley[S], Stephen M. Theberge[S], Stefan Thor[S], Stephen
Thorsett[S], Stephen G. Tilley[S], Steven Timbrook[S], Stephen S.
Tobe[S], Stephanie Toering[S], Stephen T. Toy[S], Steven E. Travers[S],
Stephanie TristramNagle[S], Stephen C. Trombulak[S], Stephen J.
Trumble[S], Stephen T. Trumbo[S], Stephen W. Tuholski[S], Stephen
Urquhart[S], Stephen Garrett Vail[S], Steven M. Vamosi[S], Steve Vander
Wall[S], Steven Verhey[S], Steven E. Vigdor[S], Steven B. Vik[S],
Stephen P. Vives[S], Steven Vogel[S], Stephen F. Walker[S], Stephen
Walton[S], Stephen Jay Warburton[S], Stephen R. Wassell[S], Steven
Alexander Wasserman[S], Steve Waters[S], Steve Weaver[S], Stephen
Webb[S], Stephen C. Weeks[S], Steven Weinberg[S],[N], Stephen
Weiner[S], Stephen H. White[S], Steve R. White[S], Steven C. Wiest[S],
Stephen J. Willson[S], Stephen W. Wilson[S], W. Stephen Wilson[S],
Steven J. Wolf[S], Stefan Leo Wolff[S], Stephen M. Wolniak[S], Stephen
D. Wolpe[S], Stephen A. Wood[S], Stephen C. Wood[S], Steven T.
Wooldridge[S], Stephen Wroe[S], Stephen L. Wust[S], Stephen John
Wylie[S], Stephen P. Yanoviak[S], Steven Yantis[S], Stephen M.
Yezerinac[S], Steven L. Youngentob[S], Stephan A. Zdancewic[S], Stephan
I. Zeeman[S], Stephen L. Zegura[S],1
*  National Center for Science Education,
http://www.ncseweb.org, S  Project Steve "Steve",
http://www.ncseweb.org/article.asp?category=18, N  Nobel laureate,
%  Appeared on The Simpsons, $  Ordered 16 Project Steve tshirts
in order to outfit all of the staff in his lab, !  Not to be
confused with the preceding Steve with the identical name.
"The Morphology of Steve", Annals of
Improbable Research, JulyAugust (2004)

Abstract:
This
report is part of Project
Steve. Project Steve is, among other things, the
first
scientific
analysis of the sex, geographiclocation, and body size of scientists
named
Steve. We performed this research for the best of all reasons:
we
discovered
that we had lots of data. No scientist can resist the
opportunity to
analyze
data, regardless of where that data came from
or why it was gathered.
 J.M. Garcia Ruiz, S.T. Hyde, A.M. Carnerup, A.G. Christy,
M.J. Van Kranendonk and N.J. Welham, "Selfassembled silicacarbonate
structures and implications for detection of ancient microfossils",
Science, 302, 11941197 (2003).

paper available here
Abstract:
We
have synthesized inorganic micronsized
filaments, whose microstucture
consists
of silicacoated nanometersized carbonate crystals,
arranged with
strong
orientational order. They exhibit noncrystallographic,
curved, helical
morphologies,
reminiscent of biological forms. The filaments are
similar to
supposed
cyanobacterial microfossils from the Precambrian
Warrawoona chert
formation
in Western Australia, reputed to be the oldest
terrestrial microfossils.
Simple
organic hydrocarbons, whose sources may also be abiotic and
indeed
inorganic,
readily condense onto these filaments and subsequently
polymerize
under
gentle heating to yield kerogenous products. Our results
demonstrate
that
abiotic and morphologically complex microstructures that are
identical to
currently
accepted biogenic materials can be synthesized
inorganically.
(see
also comments in Science
(News
of the Week), 302, 1134, 2003; see also New Scientist, 22
November, 1415, 2003;
Chemical
& Engineering News,17 November, 58, 2003.)
 G. E. Schröder, S.J. Ramsden, A.G. Christy and S.T.
Hyde, "Medial Surfaces of
Hyperbolic Structures", European Physical Journal B, 35,
551564 (2003).

pdf
version (600 KB)
Abstract:
We
introduce a robust
algorithm for numerical computation of a medial surface and
an
associated medial graph for threedimensional shapes of arbitrary
topological and
geometric
complexity, bounded by oriented
triangulated surface manifolds in three
dimensional
Euclidean space
(domains). We apply the construction to particularly complex
``bicontinuous''
domain shapes found in molecular selfassemblies,
the cubic infinite
periodic
minimal surfaces of genus three: Gyroid
(G), Diamond (D) and Primitive (P) Surfaces.
The
medial surface is
the locus of centers of maximal
spheres wholly contained
within
the domains, i.e.~spheres which graze the surface tangentially and
are not
contained
in any other such sphere. The construction of a
medial surface is a natural
generalization
of Voronoi diagrams to
continuous surfaces. The medial surface algorithm
provides
an
explicit construction of the bounding surface patch associated with a
volume
element,
giving a robust measure of surface to volume ratios
for complex forms. It also
allows
for sensible definition of a line
graph (the medial graph), particularly useful for
volumes
consisting
of connected channels, and not reliant on symmetries of the volumes.
In
addition, the medial surface construction produces a length
associated with any point
on
the surface. Variations of this length
give a useful global measure of homogeneity of the
volumes.
Comparison of medial surfaces for the P, D and G surfaces reveal the
Gyroid to be
the
most homogeneous of these cubic bicontinuous forms
(of genus three). This result is
compared
with the ubiquity of the G
surface morphology in soft mesophases, including
lyotropic
liquid
crystals and block copolymers.
 S.T.Hyde and S. Ramsden, "Some novel threedimensional
euclidean crystalline networks derived from twodimensional hyperbolic
tilings". European Physical Journal E, 31, 273284
(2003).

pdf
version (720 KB)
Abstract:
We
demonstrate the usefulness of
twodimensional hyperbolic geometry as a tool to
generate
threedimensional Euclidean (E3) networks. The technique
involves projection
from
tilings of the hyperbolic plane (H2) onto threeperiodic
minimal surfaces, embedded
in
E3. Given the extraordinary wealth of symmetries commensurate
with H2, we can
generate
networks in E3 that are difficult to construct otherwise.
In particular, we form
four,
five and sevenconnected (E3) nets containing three and
fiverings, viz. (3,7),
(5,4)
and (5,5) tilings in H2. These examples are of fundamental
interest, as they present
"topological
symmetries" that are incompatible with the isometries
of E3.
 S.T. Hyde, S. Ramsden, T. Di Matteo and J. Longdell, "Abinitio construction of some
crystalline 3D euclidean networks", Solid State Sciences,
5, 3545 (2003).

pdf
version (880 KB)
Abstract:
We
describe a technique for construction
of 3D Euclidean (E3) networks with
partiallyprescribed
rings. The
algorithm starts with 2Dhyperbolic (H2) tilings,
whose
symmetries are
commensurate with the intrinsic 2D symmetries of triply
periodic
minimal surfaces (orinfinite periodic minimal surfaces, IPMS). The 2D
hyperbolic
pattern is then projected from H2 to E3, forming 3D nets.
Examples of
cubic
and tetragonal 3connected nets with up to 288
vertices per unit cell, each
linking
a pair of 6rings and a single
8ring, are derived by projection onto the P, D,
Gyroid
and IWP
IPMS. A single example of a projection from closepacked trees in
H2
to E3 (via the D surface) is also shown, that leads to a quartet of
interwoven
equivalent
chiral nets. The configuration describes the
channel system of a novel
quadracontinuous
branched minimal surface
that is a chiral foam with four identical,
open
bubbles.
 S.T. HYDE AND G.E. SCHROEDER, "Novel Surfactant Mesostructural
Topologies: Between Lamellae and Columnar Forms". Current
Opinion in Colloid and Interface Science, 2003.

pdf version (1.7 MB)
Abstract:
Recent developments in
theoretical and experimental studies of amphiphilic lyotropic
"intermediate" mesophase formation
are summarized. For the purposes
of the review,
we consider intermediate mesophases to be
selfassemblies with novel geometries and
topologies, excluding
lamellar, sponge, columnar (hexagonal) and micellar mesophases.
Intermediates include novel
branched bilayer topologies,
enclosing multiple
interwoven channel systems and
inclined rod
packings , and punctured bilayer
morphologies,
including
mesh phases and bicontinuous monolayers.
 J.M. GARCIA RUIZ, A.G. CHRISTY, N.J. WELHAM AND S.T.HYDE, "Morphology: An ambiguous indicator
of biogenicity". Astrobiology, 2, 335351, 2002.

Abstract:
This
paper deals with the difficulty of
decoding the origins of natural structures through
the
study of their
morphological features. We focus on the case of primitive life
detection,
where
it is clear that the principles of comparative
anatomy cannot be applied. A range of
inorganic
processes are
described, that result in morphologies emulating biological shapes.
We
focus on geochemically plausible processes, in particular, the
formation of inorganic
biomorphs
in alkaline silicarich
environments, which are described in detail.
 B. CHEN, M. EDDAOUDI, S.T. HYDE, M. O'KEEFFE AND O.M. YAGHI,
"Interwoven metalorganic
framework on a periodic minimal surface with extralarge pores".
Science, vol. 291, pp. 10211023, Feb. 9 2001.

Abstract:
Interpenetration
(catenation) has long
been considered a major impediment in
the
achievement of stable and
porous crystalline structures. A strategy for the
design
of highly
porous and structurally stable networks makes use of metalorganic
building
blocks that can be assembled on a triply periodic Pminimal
geometric
surface
to produce structures that are
interpenetratingmore accurately considered
as
interwoven. We used
4,4',4"benzene1,3,5triyltribenzoic acid (H3BTB),
copper(II)
nitrate, and N,N'dimethylformamide (DMF) to prepare
Cu3(BTB)2(H2O)3·(DMF)9(H2O)2
(MOF14), whose structure reveals a
pair of interwoven
metalorganic
frameworks that are mutually
reinforced. The structure contains
remarkably
large pores, 16.4
angstroms in diameter, in which voluminous
amounts
of gases and
organic solvents can be reversibly sorbed.
 S.T.HYDE, "Identification
of lyotropic liquid crystalline mesophases". Chap. 16 of Handbook
of Applied Surface and Colloid Chemistry, (K. Holmberg, ed.),, pp.
10211023, J. Wiley & Sons, pp. 299332, 2001.

Summary:
The
Chapter is a comprehensive account of
the current state of awareness of
lyotropic
liquid crystalline
mesophases, including lamellar, cubic (bicontinuous
and
discrete),
hexagonal and intermediate mesophases, as well as sponge phases
and
microemulsions. The emphasis is on a rigorous identification of the
bilayer topology .
Some
discussion of possible &endash; as
yet unknown &endash; novel mesophases is
present.
The chapter
also contains a survey of practical techniques to identify distinct
mesophases
in the lab, including SAXS, optical microscopy and other
techniques.
 S.T.
HYDE AND S. RAMSDEN, "Polycontinuous
morphologies and interwoven helical networks". Europhysics
Letters, vol. 50(2), pp.135141, 2000.

Abstract:
We
describe a construction procedure for
polycontinuous structures, giving generalisations
of
bicontinuous
morphologies to more than two equivalent, continuous and interwoven
subvolumes.
The construction gives helical windings of disjoint
graphs on triply periodic
hyperbolic
surfaces, whose universal cover
in the hyperbolic plane consists of packed, parallel
trees.
The
simplest tri, quadra and octacontinuous morphologies consist of
three $(8,3)c$,
four
$(10,3)a$ and eight $(10,3)a$ interwoven
networks respectively. The quadra and
octacontinuous
cases are
chiral. A novel chiral bicontinuous structure is also derived,
closely
related
to the wellknown cubic gyroid mesophase.
 S.T. HYDE AND C. OGUEY, "From 2D hyperbolic forests to 3D
euclidean entangled thickets". European Physical Journal B,
vol. 16, pp. 613630, 2000.

Abstract:
A
method is developed to construct and
analyse a wide class of graphs embedded in
Euclidean
3D space,
including multiplyconnected and entangled examples. The
graphs
are
derived via embeddings of infinite families of trees (forests) in the
hyperbolic
plane, and subsequent folding into triply periodic minimal
surfaces,
including
the P, D, gyroid and H surfaces. Some of these
graphs are natural
generalisations
of bicontinuous topologies to bi,
tri, quadra and octacontinuous
forms.
Interwoven layer graphs and
periodic sets of finite clusters also emerge
from
the algorithm. Many
of the graphs are chiral. The generated graphs are
compared
with some
organometallic molecular crystals with multiple frameworks
and
molecular mesophases found in copolymer melts.
 S.T. HYDE AND S. RAMSDEN, "Chemical frameworks and hyperbolic
tilings". DIMACS Series in Discrete Mathematics and
Theoretical Computer Science, vol. 51, Discrete Mathematical
Chemistry, pp. 203224, 2000.

Abstract:
Many
complex crystalline 3dimensional
graphs are of interest to solidstate chemists,
in
order to relate
atomic and molecular crystal structures.Some of those graphs can be
generated
from tessellations of the 2d hyperbolic plane, and then
mapped onto triply
periodic
hyperbolic surfaces. The properties of
such graphs, including their densities,
can
be analyses in terms of
topological and noneuclidean geometric concepts.
Examples
include a
variety of zeolite frameworks and novel graphitic carbon structures.
 A. FOGDEN AND S.T. HYDE, "Continous transformations of cubic
minimal surfaces". European Physical Journal B, vol. 7,
pp. 91104, 1999.

Abstract:
Although
the primitive (P), diamond (D)
and gyroid (G) minimal surfaces form the
structural
basis for a
multitude of selfassembling phases, such as the bicontinuous
cubics,
relatively little is known regarding their geometrical
transformations, beyond
the
existence of the Bonnet isometry. Here
their highest symmetry deformation modes,
the
rhombohedral and
tetragonal distortions, are fully elucidated to provide a unified
description
of these simplest minimal surface families, with all
quantities expressed in
terms
of complete elliptic integrals. The
rhombohedral distortions of the gyroid are
found
to merge
continuously with those which bridge the P and D surfaces, furnishing
direct
transformations between all three cubics, preserving both
topology and zero mean
curvature
throughout. The tetragonal
distortions behave analogously, offering an
alternative
route from
the gyroid to the D surface. The cell axis ratios, surface areas and
Gaussian
curvature moments of all families are given, supplying the
necessary geometrical
input
to a curvature energy description of
cubic and intermediate phase stability.
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