Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Curvature and velocity of methane-air Bunsen flame tips.

PIV and photographic recording are used to measure the velocity of the fresh gas and the shape of the reaction layer in a region around the tip of a methane-air Bunsen flame attached to a cylindrical burner. The results compare well with numerical simulations carried out with an infinite activation energy reaction model. The experimental and numerical results confirm that the well-known linear relation between flame velocity and flame stretch derived from asymptotic theory for weakly curved and strained flames is valid for small and moderate values of the flame stretch if the modified definition of stretch introduced by Echekki and Mungal (Proc Combust Inst 23:455–461, 1990) and Poinsot et al. (Combust Sci Technol 81:45–73, 1992) is used. However, the relation between flame velocity and modified stretch ceases to be linear and approaches a square root law for large values of the stretch, when the curvature of the flame tip becomes large compared to the inverse of the thickness of a planar flame.

Optimal Multiresolution 3D Level-Set Method for Liver Segmentation incorporating Local Curvature Constraints

Advanced liver surgery requires a precise pre-operative planning, where liver segmentation and remnant liver volume are key elements to avoid post-operative liver failure. In that context, level-set algorithms have achieved better results than others, especially with altered liver parenchyma or in cases with previous surgery. In order to improve functional liver parenchyma volume measurements, in this work we propose two strategies to enhance previous level-set algorithms: an optimal multi-resolution strategy with fine details correction and adaptive curvature, as well as an additional semiautomatic step imposing local curvature constraints. Results show more accurate segmentations, especially in elongated structures, detecting internal lesions and avoiding leakages to close structures

Curvature and velocity of methane-air Bunsen flame tips

PIV and photographic recording are used to measure the velocity of the fresh gas and the shape of the reaction layer in a region around the tip of a methane- air Bunsen flame attached to a cylindrical burner. The results compare well with numerical simulations carried out with an infinite activation energy reaction model. The experimental and numerical results confirm that the well-known linear relation between flame velocity and flame stretch derived from asymptotic theory for weakly curved and strained flames is valid for small and moderate values of the flame stretch if the modified definition of stretch introduced by Echekki and Mungal (Proc Combust Inst 23:455–461,1990) and Poinsot et al. (Combust Sci Technol 81:45–73,1992) is used. However, the relation between flame velocity and modified stretch ceases to be linear and approaches a square root law for large values of the stretch, when the curvature of the flame tip becomes large compared to the inverse of the thickness of a planar flame

Concrete Swelling in a Double Curvature Dam

Se describe el problema del hinchamiento del hormigón en las presas de doble curvatura. Several chemical reactions are able to produce swelling of concrete for decades after its initial curing, a problem that affects a considerable number of concrete dams around the world. The object of the work reported is to simulate the underlying mechanisms with sufficient accuracy to reproduce the past history and to predict the future evolution reliably. Having studied the available formulations, that considered to be more promising was adopted and introduced via user routines in a commercial finite element code. It is a non isotropic swelling model,compatible with the cracking and other non-linearities displayed by the concrete. The paper concentrates on the work conducted for a double-curvature arch dam. The model parameters were determined on the basis of some parts of the dam’s monitored histories, reliability was then verified using other parts and, finally, predictions were made about the future evolution of the dam and its safety margin.

Effect of impacting radius of curvature on firmness sensing of fruits in a sorting system.

Fruits of two varieties of both apples and pear were tested to measure their response to small energy impact applied by a impact tester with two spherical tips of different radious of curvature ( RA = 2.48 cm and RB = 0.98 cm) and equal mass were used. In the four varieties studied, the size of bruise was smaller with a spherical tip RA than with tip RB . The non-destructive impact test would cause less damage with a spherical impactor with a radious bigger than 0.98 cm.

Experimental study on bridge damage identification based on wavelet packet energy curvature difference method

Among those damage identification methods, the Wavelet Packet Energy Curvature Difference (WPECD) Method is an effective one. However, most of the existing methods rely on numerical simulation and are unverified via experiment, and very few of them have been applied to practice. In this paper, the validity of WPECD in structural damage identification is verified by a numerical example. A damage simulation experiment is taken on a real replaced girder at the Ziya River New Bridge in Cangzhou. Two damage cases are applied and the acceleration responses at the measuring points are obtained, based on which the damages are identified with the WPECD Method, and the influence of wavelet function and decomposition level is studied. The results show that the WPECD Method can identify structure damage efficiently and can be put into practice.

Methodology of quantifying curvature of Fresnel lenses and its effect on CPV module performance

Fresnel lenses used as primary optics in concentrating photovoltaic modules may show warping produced by lens manufacturing or module assembly (e.g., stress during molding or weight load) or due to stress during operation (e.g., mismatch of thermal expansion between different materials). To quantify this problem, a simple method called “checkerboard method” is presented. The proposed method identifies shape errors on the front surface of primary lenses by analyzing the Fresnel reflections. This paper also deals with the quantification of the effects these curvatures have on their optical performance and on the electrical performance of concentrating modules incorporating them. This method can be used to perform quality control of Fresnel lenses in scenarios of high volume production.

Phalangeal curvature and positional behavior in extinct sloth lemurs (Primates, Palaeopropithecidae)

Recent paleontological discoveries in Madagascar document the existence of a diverse clade of palaeopropithecids or “sloth lemurs”: Mesopropithecus (three species), Babakotia (one species), Palaeopropithecus (three species), and Archaeoindris (one species). This mini-radiation of now extinct (“subfossil”) lemurs is most closely related to the living indrids (Indri, Propithecus, and Avahi). Whereas the extant indrids are known for their leaping acrobatics, the palaeopropithecids (except perhaps for the poorly known giant Archaeoindris) exhibit numerous skeletal design features for antipronograde or suspensory positional behaviors (e.g., high intermembral indices and mobile joints). Here we analyze the curvature of the proximal phalanges of the hands and feet. Computed as the included angle (θ), phalangeal curvature develops in response to mechanical use and is known to be correlated in primates with hand and foot function in different habitats; terrestrial species have straighter phalanges than their arboreal counterparts, and highly suspensory forms such as the orangutan possess the most curved phalanges. Sloth lemurs as a group are characterized by very curved proximal phalanges, exceeding those seen in spider monkeys and siamangs, and approaching that of orangutans. Indrids have curvatures roughly half that of sloth lemurs, and the more terrestrial, subfossil Archaeolemur possesses the least curved phalanges of all the indroids. Taken together with many other derived aspects of their postcranial anatomy, phalangeal curvature indicates that the sloth lemurs are one of the most suspensory clades of mammals ever to evolve.

Mapping the intrinsic curvature and flexibility along the DNA chain

The energy of DNA deformation plays a crucial and active role in its packaging and its function in the cell. Considerable effort has gone into developing methodologies capable of evaluating the local sequence-directed curvature and flexibility of a DNA chain. These studies thus far have focused on DNA constructs expressly tailored either with anomalous flexibility or curvature tracts. Here we demonstrate that these two structural properties can be mapped also along the chain of a “natural” DNA with any sequence on the basis of its scanning force microscope (SFM) images. To know the orientation of the sequence of the investigated DNA molecules in their SFM images, we prepared a palindromic dimer of the long DNA molecule under study. The palindromic symmetry also acted as an internal gauge of the statistical significance of the analysis carried out on the SFM images of the dimer molecules. It was found that although the curvature modulus is not efficient in separating static and dynamic contributions to the curvature of the population of molecules, the curvature taken with its direction (its sign in two dimensions) permits the direct separation of the intrinsic curvature from the flexibility contributions. The sequence-dependent flexibility seems to vary monotonically with the chain's intrinsic curvature; the chain rigidity was found to modulate as its local thermodynamic stability and does not correlate with the dinucleotide chain rigidities evaluation made from x-ray data by other authors.

Curvature Induced by Amyloplast Magnetophoresis in Protonemata of the Moss Ceratodon purpureus1

After gravistimulation of Ceratodon purpureus (Hedw.) Brid. protonemata in the dark, amyloplast sedimentation was followed by upward curvature in the wild-type (WT) and downward curvature in the wwr mutant (wrong way response). We used ponderomotive forces induced by high-gradient magnetic fields (HGMF) to simulate the effect of gravity and displace the presumptive statoliths. The field was applied by placing protonemata either between two permanent magnets at the edge of the gap, close to the edge of a magnetized ferromagnetic wedge, or close to a small (<1 mm) permanent magnet. Continuous application of an HGMF in all three configurations resulted in plastid displacement and induced curvature in tip cells of WT and wwr protonemata. WT cells curved toward the HGMF, and wwr cells curved away from the HGMF, comparable to gravitropism. Plastids isolated from protonemal cultures had densities ranging from 1.24 to 1.38 g cm−3. Plastid density was similar for both genotypes, but the mutant contained larger plastids than the WT. The size difference might explain the stronger response of the wwr protonemata to the HGMF. Our data support the plastid-based theory of gravitropic sensing and suggest that HGMF-induced ponderomotive forces can substitute for gravity.

Autonomic Straightening after Gravitropic Curvature of Cress Roots1

Few studies have documented the response of gravitropically curved organs to a withdrawal of a constant gravitational stimulus. The effects of stimulus withdrawal on gravitropic curvature were studied by following individual roots of cress (Lepidium sativum L.) through reorientation and clinostat rotation. Roots turned to the horizontal curved down 62° and 88° after 1 and 5 h, respectively. Subsequent rotation on a clinostat for 6 h resulted in root straightening through a loss of gravitropic curvature in older regions and through new growth becoming aligned closer to the prestimulus vertical. However, these roots did not return completely to the prestimulus vertical, indicating the retention of some gravitropic response. Clinostat rotation shifted the mean root angle −36° closer to the prestimulus vertical, regardless of the duration of prior horizontal stimulation. Control roots (no horizontal stimulation) were slanted at various angles after clinostat rotation. These findings indicate that gravitropic curvature is not necessarily permanent, and that the root retains some commitment to its equilibrium orientation prior to gravitropic stimulation.

The effects of sequence context on DNA curvature.

Recent experiments have exposed significant discrepancies between experimental data and predictive models for DNA structure. These results strongly suggest that DNA structural parameters incorporated in the models are not always sufficient to account for the influence of sequence context and of specific ion effects. In an attempt to evaluate these two effects, we have investigated repetitive DNA sequences with the sequence motif GAGAG.CTCTC located in different helical phasing arrangements with respect to poly(A) tracts and GGGCCC.GGGCCC sequence motifs. Methods used are ligase-mediated cyclization and gel mobility experiments along with DNase I cutting and chemical probe studies. The results provide new evidence for curvature in poly(A) tracts. They also show that the sequence context in which bending and flexible sequence elements are found is an important aspect of sequence-dependent DNA conformation. Although dinucleotide models generally have good predictive power, this work demonstrates that in some instances sequence elements larger than the dinucleotide must be taken into account, and hence it provides a starting point for the appropriate modification and refinement of existing structural models for DNA.

Image processing via level set curvature flow.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.