Publications (129)311.92 Total impact

Article: Autorotation

Article: Autorotation, Invited Comment
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ABSTRACT: A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plusminus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake  [Show abstract] [Hide abstract]
ABSTRACT: The properties of doublestranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular microDNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular microDNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular microDNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented. 
Article: Ribbon Crystals
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ABSTRACT: A repetitive crystallike pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This construction defines a differentiable frame, the ribbon frame, which does not have singular points, whereby we avoid the shortcomings of the FrenetSerret frame. The observed spontaneous pattern is modeled using planar triangles and cylindrical arcs, and the ribbon structure is shown to arise from a maximization of the endtoend length of the ribbon, i.e. from an optimal use of ribbon length. The phenomenon is discussed in the perspectives of incompatible intrinsic geometries and of the emergence of longrange order.  [Show abstract] [Hide abstract]
ABSTRACT: Two separate regimes exist for the aspect ratio of DNA. A low aspect regime where DNA will twist further under strain and a high aspect regime where DNA will untwist under strain. The question of the overall geometry, i.e. the aspect ratio, of DNA is revisited from the perspective of a geometrical analysis of transcription. It is shown that under certain reasonable assumptions transcription is only possible if the aspect ratio is in the regime corresponding to further twisting. We find this constraint to be in agreement with longestablished crystallographic studies of DNA. 
Article: A principle for ideal torus knots
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ABSTRACT: We study simple, knotted and linked torus windings that are made of tubes of finite thickness. Knots which have the shortest rope length are often denoted ideal structures. Conventionally, the ideal structure are found by rope shortening routines. It is shown that alternatively they can be directly determined as maximally rotated structures. In many cases these structures are also zerotwist structures i.e. structures that neither rotate one or the other way under strain. We use this principle to implement rapid numerical calculations of the ideal structures and subsequently quantify them by their aspect ratio. The results are compared with the aspect ratios of biological torus molecules.  [Show abstract] [Hide abstract]
ABSTRACT: Helical structures with LennardJones selfinteractions are studied for optimal conformations. For this purpose, their selfenergy is analyzed for extrema with respect to the geometric parameters of the helices. It is found that LennardJones helices exhibit a first order phase transition from a state with large curvature of the helical backbone to one with a small curvature. I.e. from a dense helix to an extended helix. A transition from one helical structure to another is a phenomenon known to take place in selfassembling helices formed in multicomponent solutions with cholesterol. 
Article: Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA
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ABSTRACT: The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Studies of molecules that are intrinsically chiral, such as doublestranded DNA, is one example. Their properties generally depend on the local geometry, i.e. on curvature and torsion, yet the paths of closed molecules are globally restricted by topology. Molecules that fulfill a twist neutrality condition, a zero sum rule for the incremental change in the rate of winding along the curve, will behave neutrally to strain. This has implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be doublestranded. It also follows that all microDNAs longer than the minimum length must be concave. This counterintuitive result is consistent with the kinklike appearance which has been observed for circular DNA. A prediction for the total negative curvature of a circular microDNA is given as a function of its length.  [Show abstract] [Hide abstract]
ABSTRACT: The newly proposed closepacked motif for collagen and the more established 7/2 structure are investigated and compared. Firstprinciples semiempirical wave function theory and KohnSham density functional theory are applied in the study of these relatively large and complex structures. The structures are refined, and comparable stability is displayed using these methods. The electronic circular dichroism of the closepacked model is shown to have a significant negative bias and a large signal. This bias is consistent with existing experimental data, though it is not unambiguously possible from the circular dichroism calculations to select one structure over the other. An interesting feature of the closepacked structure is the existence of a central channel. Simulations show that, if hydrogen atoms are placed in the cavity, a chain of molecular hydrogens is formed suggesting a possible biological function for molecular hydrogen.  [Show abstract] [Hide abstract]
ABSTRACT: This article reports on studies of the chemical alterations induced by synchrotron radiation at the calciteethanol interface, a simple model system for interfaces between minerals and more complex organic molecules containing OH groups. A combination of Xray reflectivity and Xray photoelectron spectroscopy of natural calcite, cleaved in distilled ethanol to obtain new clean interfaces, indicated that, during a 5 h period, the two top atomic layers of calcite, CaCO(3), transform into calcium oxide, CaO, by releasing CO(2). Also, the occupation of the first ordered layer of ethanol attached to calcite by hydrogen bonds almost doubles. Comparison between radiated and nonradiated areas of the same samples demonstrate that these effects are induced only by radiation and not caused by aging. These observations contribute to establishing a time limit for synchrotron experiments involving fluidmineral interfaces where the polar OH group, as present in ethanol, plays a key role in their molecular structure and bonding. Also, the chemical evolution observed in the interface provides new insight into the behavior of some complex organic molecules involved in biomineralization processes.  [Show abstract] [Hide abstract]
ABSTRACT: The question of the value of the pitch angle of DNA is visited from the perspective of a geometrical analysis of transcription. It is suggested that for transcription to be possible, the pitch angle of BDNA must be smaller than the angle of zerotwist. At the zerotwist angle the double helix is maximally rotated and its straintwist coupling vanishes. A numerical estimate of the pitch angle for BDNA based on differential geometry is compared with numbers obtained from existing empirical data. The crystallographic studies shows that the pitch angle is approximately 38 deg., less than the corresponding zerotwist angle of 41.8 deg., which is consistent with the suggested principle for transcription.  [Show abstract] [Hide abstract]
ABSTRACT: The diameter of the nucleosome core particle is the same for all the eukaryotes. Here we discuss the possibility that this selectiveness is consistent with a propensity for twist neutrality, in particular, for the double helical DNA to stay rotationally neutral when strained. Reorganization of DNA cannot be done without some level of temporal tensile stress, and as a consequence chiral molecules, such as helices, will twist under strain. The requirement that the nucleosome, constituting the nucleosome core particle and linker DNA, has a vanishing straintwist coupling leads to a requirement for the amount of bending. For the diameter of the coiled DNA we obtain the relatively accurate numerical estimate of 2R=82 Å.  [Show abstract] [Hide abstract]
ABSTRACT: Two important geometrical properties of Nhelix structures are influenced by bending. One is maximizing the volume fraction, which is called optimalpacking, and the other is having a vanishing straintwist coupling, which is called zerotwist. Zerotwist helices rotate neither in one nor in the other direction under pull. The packing problem for tubular Nhelices is extended to bent helices where the strands are coiled on toruses. We analyze the geometry of open circular helices and develop criteria for the strands to be in contact. The analysis is applied to a single, a double and a triple helix. General Nhelices are discussed, as well as zerotwist helices for N > 1. The derived geometrical restrictions are gradually modified by changing the aspect ratio of the torus.  [Show abstract] [Hide abstract]
ABSTRACT: A broad tablelike entropy change (ΔS) at room temperature has been observed in the ferromagnetic compound La0.75Ca0.15Sr0.10MnO3, which is analyzed in the concept of Landau theory and with critical exponent analysis obtained from the magnetization measurements. The change in entropy in La0.75Ca0.15Sr0.10MnO3 is discussed in the light of magnetoelastic coupling between the magnetization and the lattice distortion. Application aspects of this unusual broad magnetocaloric effect with relative cooling power of 107 J kg−1 in an applied magnetic field of 1.6 T with an operating temperature range of 93 K around the room temperature are also discussed.  [Show abstract] [Hide abstract]
ABSTRACT: To produce biominerals, such as shells, bones, and teeth, living beings create organic compounds that control the growth of the solid phase. Investigating the atomic scale behavior of individual functional groups at the mineralfluid interface provides fundamental information that is useful for constructing accurate predictive models for natural systems. Previous investigations of the activity of coccolithassociated polysaccharides (CAP) on calcite, using atomic force microscopy (AFM) [Henriksen, K., Young, J. R., Bown, P. R., and Stipp, S. L. S. Palentology 2004, 43 (Part 3), 725743] and molecular dynamics (MD) modeling [Yang, M., Stipp, S. L. S., and Harding, J. H. Cryst. Growth Des. 2008, 8 (11), 40664074], have suggested that OH functional groups control polysaccharide attachment. The purpose of this work was to characterize, using Xray reflectivity (XR) combined with molecular dynamics (MD) simulations, the structuring on calcite of a layer of the simplest carbon chain molecule that contains an OH group, ethanol (CH(3)CH(2)OH). We found evidence that EtOH forms a highly ordered structure at the calcite surface, where the first layer molecules bond with calcite. The ethanol molecules stand up perpendicularly at the interface or nearly so. As a consequence, the fatty, CH(3) ends form a new surface, about 6 Å from the termination of the bulk calcite, and beyond that, there is a thin gap where ethanol density is low. Following is a more disordered layer that is two to three ethanol molecules thick, about 14 Å, where density more resembles that of bulk liquid ethanol. The good agreement between theory and experiment gives confidence that a theoretical approach can offer information about behavior in more complex systems. 
Article: The size of the nucleosome
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ABSTRACT: The structural origin of the size of the 11 nm nucleosomal disc is addressed. On the nanometer lengthscale the organization of DNA as chromatin in the chromosomes involves a coiling of DNA around the histone core of the nucleosome. We suggest that the size of the nucleosome core particle is dictated by the fulfillment of two criteria: One is optimizing the volume fraction of the DNA double helix; this requirement for closepacking has its root in optimizing atomic and molecular interactions. The other criterion being that of having a zero straintwist coupling; being a zerotwist structure is a necessity when allowing for transient tensile stresses during the reorganization of DNA, e.g., during the reposition, or sliding, of a nucleosome along the DNA double helix. The mathematical model we apply is based on a tubular description of double helices assuming hard walls. When the basepairs of the linkerDNA is included the estimate of the size of an ideal nucleosome is in close agreement with the experimental numbers. Interestingly, the size of the nucleosome is shown to be a consequence of intrinsic properties of the DNA double helix. 
Article: Lead inclusions in aluminum
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ABSTRACT: Synchrotron Xray reflectivity (SXR) was used to measure the thickness of the water film that adsorbs on a {} cleavage surface of calcite (CaCO3) in a sample chamber where relative humidity could be controlled within the range from <4% to 90%. Gases used to carry water vapour were initially either 100% N2 or 100% CO2. The product water film was remarkably constant in thickness at 15.5 Å (±1 Å) and independent of humidity. When N2 was used as the carrier gas, this film displayed a gap in its electron density at between 0.6 and 2 Å distance from the calcite surface, depending on humidity. This implies that a change in the arrangement of water molecules occurs in direct proximity to the surface. This electron density discontinuity was measurably further from the calcite surface, at 3.4 Å, when CO2 was used as the carrier gas. Except for this thin low density region proximate to the calcite surface, the density of the adsorbed water layer was 0.9 g cm−3, therefore suggesting a significant degree of ordering. Atomic force microscopy (AFM) images were completed in conjunction with the SXR measurements on similarly prepared calcite cleavage surfaces. AFM showed that terraces may be atomically flat over 1 μm or more. SXR corroborated this observation, with results showing that carefully cleaved surfaces had a starting root mean square (r.m.s.) roughness of ∼1.2 Å. Diffuse scatter measurements constrained the correlation lengths of these surfaces to be at least 18,000 Å. For comparison with the cleaved samples, a surface was also prepared by chemomechanical Syton polishing. This surface gave an r.m.s roughness by SXR that was an order of magnitude higher, equal to 12.1 Å. In this case, diffuse scatter resolved a correlation length of 950 Å, and revealed a fractal dimension that was higher than for the cleaved surface. On Syton polished samples, the water film determined by SXR was about twice as thick as for freshly cleaved surfaces, with a density of 1.0 g cm−3, equal to that of bulk water. However, surface roughness was too large to allow resolution of any gap in the electron density within the water layer proximate to the solid surface. Our AFM observations also confirm previous reports of calcite surface recrystallization. The electron density of the solid surface determined by SXR is indistinguishable from that of calcite, indicating that any material recrystallized within the adsorbed water film is compositionally indistinguishable from the calcite substrate.  [Show abstract] [Hide abstract]
ABSTRACT: The paircorrelations between the positions of the six known planets in the exoplanetary system HD 10180 are studied. There are six nontrivial and almost equally spaced peaks. This demonstrates longerranged positional order between the orbits and suggests a seventh orbit at 0.92 AU that is consistent with these correlations. Comment: 5 pages, 4 figures  [Show abstract] [Hide abstract]
ABSTRACT: Many hoards found in Ireland, Scotland, Orkney Islands, and Scandinavia demonstrate the vikings ability to fabricate beautiful arm and neck rings of twisted silver and gold rods. Characteristic for such rings is the uniform appearance of the twisted pattern along the length of the arm ring, as well as from one arm ring to another, also when found at distant geographical locations. How can the appearance of the twisted wires be so perfectly repetitive? We demonstrate that the answer is that the vikings utilized a selfforming motif: The pattern arises from a twisting of the wires to a maximally rotated configuration. That is why the twist patterns in these arm and neck rings are beautiful, repetitive, and universal. Comment: 4 pages, 3 figures
Publication Stats
4k  Citations  
311.92  Total Impact Points  
Top Journals
Institutions

19952013

Technical University of Denmark
 • National Laboratory for Sustainable Energy
 • Department of Physics
Lyngby, Capital Region, Denmark


1996

Lomonosov Moscow State University
Moskva, Moscow, Russia 
Copenhagen University Hospital Hvidovre
 Department of Infectious Diseases
Hvidovre, Capital Region, Denmark


1993

Odense University Hospital
Odense, South Denmark, Denmark


19851988

Brookhaven National Laboratory
 Physics Department
New York, New York, United States 
Harvard University
 Department of Physics
Cambridge, Massachusetts, United States
