Degenerate Deformation Research Articles

Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations

Let (M,I,Ω) be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration π:M↦X, and η a closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π⁎η is again a holomorphically symplectic form, for another complex structure I′, which is uniquely determined by Ω′. The corresponding deformation of complex structures is called “degenerate twistorial deformation”. The map π is holomorphic with respect to this new complex structure, and X and the fibers of π retain the same complex structure as before. Let s be a smooth section of π. We prove that there exists a degenerate twistorial deformation (M,I′,Ω′) such that s is a holomorphic section.

Anisotropic swelling of anisotropic elastic panels.

While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial sheet materials. In this theoretical work, we consider central swelling and shrinkage of plates of aspect ratio and material properties relevant to the manufacture of engineered wood composite panels in which both in-plane swelling and material stiffness are highly orthotropic, leading to multiple separations in energy scales. With transverse swelling in the soft direction, and gradients in the stiff direction, the warped plates adopt two distinct types of configurations, axisymmetric and twisted, which we illustrate with toy models. We employ a two-parameter family of isometries to embed the metric programmed by the swelling, thus reducing the problem to one of minimizing bending energy alone. A simple argument is seen to closely predict averaged axisymmetric curvatures. While purely cylindrical shapes are unobtainable by pure in-plane swelling, they can be closely approximated in a highly anisotropic system. However, anisotropy can favor twisting, and breaks a degenerate soft deformation mode associated with minimal surfaces in isotropic materials. Bifurcations from axisymmetric to twisted shapes can be induced by anisotropy or by certain attributes of a central shrinkage profile. Finally, we note how our findings indicate practical limitations on the diagnosis of moisture inhomogeneities in manufactured panels by observation of warped conformations, due to the sensitivity of the qualitative response to specifics of the profile.

Closed‐Form Expressions of Seismic Deformation in a Homogeneous Maxwell Earth Model

AbstractEarthquake activities involve coseismic and postseismic deformations, and these seismic deformations can be computed using corresponding dislocation theories. However, conventional dislocation theories are usually given using numerical dislocation Love numbers and numerical Green's functions. In this study, we present explicit expressions of the time‐dependent dislocation Love numbers for a point source in a homogeneous viscoelastic (Maxwell rheology) spherical Earth model and the displacement Green's functions. Other surface variables, such as tilt and strain, can be obtained in a similar manner. The analytical Green's functions are derived from the degenerate deformation system without considering self‐gravitation. The Green's functions can be applied to efficiently compute viscoelastic seismic and volcanic deformations in an approximate manner.

Non-Rigid Structure-From-Motion on Degenerate Deformations With Low-Rank Shape Deformation Model

Non-rigid structure-from-motion (NRSfM) is the process of recovering time-varying 3D structures and poses of a deformable object from an uncalibrated monocular video sequence. Currently, most NRSfM algorithms utilize a non- degenerate assumption for non-rigid object deformations whereby the 3D structures of a non-rigid object can be assumed to be a linear combination of basis shapes with full rank three. Unfortunately, this assumption will produce extra degrees-of-freedom when the non-rigid object has some degenerate deformations with shape bases of rank less than three. These extra degrees-of-freedom will yield spurious shape deformations due to non-negligible noise in real applications, which will cause substantial reconstruction errors. To solve this problem, we propose a low-rank shape deformation model to represent 3D structures of degenerate deformations. When modeling degenerate deformations, the proposed model exploits the rank-deficient nature of degenerate deformations in addition to the low-rank property of non-rigid objects' trajectories, thus providing a more accurate and compact representation compared with existing models. Based on this model, we formulate the NRSfM problem as two coherent optimization problems. These problems are solved with iterative non-linear optimization algorithms. Experiments on synthetic and motion capture data are conducted. The results exhibit the significant advantages of our approach over state-of-the-art NRSfM algorithms for the 3D recovery of non-rigid objects with degenerate deformations.

On pseudorotation

Pseudorotation was introduced as a molecular motion related to degenerate ring deformation modes in ring systems. This motion is related to the motion of a particle on a ring and is, therefore, called a one-dimensional pseudorotation. This motion is related either to ring puckering or to the fluctuation of weak bonds. It is shown that there are systems where bond fluctuation occurs on the surface of polyhedra which are related to the motion of a particle on a sphere. We call these bond fluctuations two-dimensional pseudorotation and give the energy expressions for a free two-dimensional pseudorotation. One-dimensional pseudorotation is thoroughly discussed and shown how one can calculate the symmetry number of pseudorotation. We discuss systems where two-dimensional pseudorotation can be expected such as bullvalene or vacancies in solids with strong bond fluctuations.

HEAT KERNEL OF NONMINIMAL GAUGE FIELD KINETIC OPERATORS ON MOYAL PLANE

We generalize the Endo formula1 originally developed for the computation of the heat kernel asymptotic expansion for nonminimal operators in commutative gauge theories to the noncommutative case. In this way, the first three nonzero heat trace coefficients of the nonminimal U (N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U (1) sector of the gauge model. The nonplanar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space–time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce nonlocal gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U (N) model at one-loop level. Such phenomenon was observed at first in Ref. 2 for spacelike noncommutative ϕ4 scalar and U (1) gauge theories. The twisted-gauge transformation approach is discussed.

On Some Degenerate Deformations of Commutative Polynomial Algebras

This paper gives a classification of the prime ideals, primitive ideals, and irreducible representations of where K is an algebraically closed field, n ≥ 3, and β ij ∈ K. The classification of the prime ideals of S proves that, under the Zariski topology, the topological dimension of spec S is no greater than the Gelfand-Kirillov dimension of S. Included is an appendix by A. Berliner, in which it is shown that the finite dimensional irreducible representations are all one-dimensional.

Resonant infrared laser-induced desorption of methane condensed on NaCl(100): Isotope mixture experiments

Resonantly enhanced infrared laser-induced desorption of methane condensed on a single-crystal NaCl(100) surface is observed after excitation with the widely tunable infrared laser output of the free-electron laser at the free-electron laser for infrared experiments facility using mass spectroscopic detection and time-of-flight analysis. Desorption of methane is observed only when the exciting light is in resonance with an internal vibrational mode of the molecule. Different intramolecular modes of the three methane isotopologues under study--CH(4), CD(4), and CD(3)H--are excited; the degenerate deformation mode nu(4) is observed for CH(4) and CD(4) at 7.69 and 10.11 microm, respectively, as well as the nu(2) and nu(4) modes of CD(3)H at 7.79, 9.75, and 9.98 microm. The desorption signals for the pure layers of these different methane isotopologues as well as for different mixtures of two of these are investigated as a function of the infrared wavelength and the laser fluence. The desorption behavior for pure and mixed layers is compared and the underlying desorption mechanism is discussed.

Seiberg duality in matrix models II

In this Letter we continue the investigation, within the context of the Dijkgraaf–Vafa programme, of Seiberg duality in matrix models as initiated in [B. Feng, hep-th/0211202], by allowing degenerate mass deformations. In this case, there are some massless fields which remain and the theory has a moduli space. With this illustrative example, we propose a general methodology for performing the relevant matrix model integrations and addressing the corresponding field theories which have non-trivial IR behaviour, and which may or may not have tree-level superpotentials.

Annealing of polyacene-based oligomer synthesized under high pressure

A polyacene-based oligomer was synthesized by reaction of diphenyldiacetylene under high pressure (pressure: 0.1 GPa; temperature: 250°C; time: 5 h). Annealing of the polyacene-based oligomer was carried out (temperature: 300–800°C; time: 5 h). Gas analysis, BET surface area measurement, Raman scattering, X-ray diffraction, elemental analysis, 13C-NMR, and conductivity measurements were performed to characterize the structure of the product. The oligomer was annealed with the appearance of mainly hydrogen. The H/C of the product decreased with increasing annealing temperature. The Raman band is observed at 1610 cm−1 assigned to a doubly degenerate deformation vibration of the carbon hexagonal ring. The additional band observed at 1340 cm−1 is attributed to the size effect. X-ray diffraction indicated that the product had no sharp peak because of the disordered carbon structure. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 289–292, 1999

Adsorption and interlayer mixing of methane on Ni(100) at 20 K

The adsorbed states of methane on Ni(100) at 20 K have been studied by IRAS and TPD. For the first layer CH 4, bands are observed at 3000, 2884 and 1298 cm −1. On the other hand, only two bands are observed at 3017 and 1304 cm −1 for the second layer CH 4. The bands between 3000 and 3017 cm −1 are assigned to the degenerate CH stretching mode (v 3), the bands between 1294 and 1304 cm −1 to the degenerate deformation mode (v 4), and the 2884 cm −1 band to the symmetric CH stretching mode (v 1), respectively. Desorption temperatures of the first layer and the second layer methane are ∼51 and ∼34 K, respectively. The observed enhanced sticking on the covered surface is due to efficient energy transfer to the adsorbate owing to mass matching. In addition, interlayer mixing between the first layer and the second layer methane takes place during the adsorption process. The enhanced interlayer mixing observed for the post-dosing of Xe on the methane covered Ni(100) surface suggests that the adsorption energy of the incoming particle plays an important role in the interlayer mixing.

Isotopically selective IR multiphoton dissociation of 1,3,5-trioxane

Searching for oxygen-isotope selectivity, we investigated the infrared multiphoton dissociation of the formaldehyde trimer around 10 µm, in a range where the molecule has a degenerate and a non-degenerate CO stretch vibration and a degenerate CH2 deformation vibration. In the region of the two latter, the wavelength dependence of the dissociation yield exhibits sharp structures. They were assigned ton-photon resonances (n = 2, 3, 5) by the help of the IR spectrum in the fundamental and overtone region. The O and C selectivities were very small (1.05) near the non-degenerate CO stretch band, but surprisingly large (2–4) in the CH2 deformation, which has no isotopic shift. The selectivity is not controlled by the first (n-photon) excitation step, but only by a later step. Its assignment is attempted. The pressure dependence of the dissociation is peculiar: Only after an initial decrease, the yield exhibits the usual rise with pressure. We attribute the decrease to a relaxation which perturbs the two-photon resonance.

The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth

The coherent transient responses of two simple molecular liquids, CS/sub 2/ and CHBr/sub 3/, are studied at room temperature with the technique of time-resolved pump/probe optical Kerr effect. Use is made of an ultrashort laser with pulsewidth varying from /spl ges/100 to 28 femtoseconds (fs). For both liquids the instantaneous electronic response is found to increase markedly relative to the delayed nuclear response as input pulse is shortened. The contribution of the coherent coupling effect to the Kerr signal near delay zero is found to be significant, and is attributed to a retarded nuclear response. The latter, along with the nonvanishing response of nuclear motion to the shortest (28 fs) input pulse, strongly suggests that nuclei are intrinsically coupled to the valence electrons. The intrinsic electron-nucleus coupling in combination with molecular symmetry satisfactorily accounts for the observation that the ultrafast nuclear Kerr response of liquid CS/sub 2/ is much stronger than the electronic one, whereas the opposite is true with liquid CHBr/sub 3/. The ultrafast response of liquid CHBr/sub 3/ also features the occurrence of vibrational quantum beats, involving as many as three normal vibrations of the CHBr/sub 3/ molecule. The normal vibrations identified from the beats are the CBr/sub 3/ symmetric deformation (/spl nu//spl tilde//sub 3/=222 cm/sup -1/) and the CBr/sub 3/ symmetric stretch (/spl nu//spl tilde//sub 6/=540 cm/sup -1/), in addition to the CBr/sub 3/ degenerate deformation (/spl nu//spl tilde//sub 6/=154 cm/sup -1/) observed in temporal domain heretofore. Both liquids also exhibit identical ultrafast intermolecular dynamics.

A GF-Matrix Approach to the End-to-End Coupling in Ethane-like Molecules

We examine the effect of end-to-end coupling on the degenerate vibrational deformations of ethane-like molecules by considering the form of the dependence of the elements of the G and F matrices on the internal rotation angle γ. This can be done by simple geometrical considerations, in a basis of internal vibrational coordinates. After transformation to symmetry coordinates belonging to different species of the G36(EM) extended molecular group, the product G(0)F(0) of the γ-independent parts of the G and F matrices is diagonalized. The resulting zero-order normal modes and their conjugate momenta are used in building up the vibration-torsion Hamiltonian, including the γ-dependent terms. We find that (i) in the case of a low barrier hindering the internal rotation the most convenient sets of degenerate normal coordinates are either Gs (in the case of a weak effect of the end-to-end coupling on the relative deformations) or E1d, E2d; (ii) degenerate vibrational coordinates whose top and frame components have at the least one common atom lead to E1d, E2d normal modes regardless of the barrier height; (iii) "unpaired" degenerate vibrational coordinates, such as the skeletal bending of dimethylzinc, always contribute an E1d normal mode; and (iv) in the case of high or moderate barriers, Gs normal modes are unlikely to occur, and the most probable normal mode symmetries are E1d, E2d.

Decomposition of silicon hydrides following disilane adsorption on porous silicon surfaces

Disilane (Si 2H 6) is used for silicon chemical vapor deposition (CVD) and is a potential precursor for atomic layer epitaxy (ALE) on silicon surfaces. In this study, Fourier transform infrared (FTIR) transmission spectroscopy was employed to examine the adsorption and decomposition of disilane on high surface area porous silicon surfaces. The FTIR spectra revealed that disilane dissociatively adsorbs on porous silicon surfaces at 200 K to form a large fraction of SiH 3 surface species and some SiH 2 and SiH surface species. The SiH x stretching modes between 2125–2156 cm −1, the SiH 3 degenerate deformation mode at 862 cm −1 and the SiH 2 scissor mode at 907 cm −1 were then employed to monitor the decomposition of the surface hybride species during thermal annealing. Between 200–600 K, the SiH 3 species decreased and were depleted from the silicon surface. Concurrently, the SiH 2 surface species were observed to increase between 200–440 K and subsequently to decrease between 440–620 K. Only monohydride species remained on the porous silicon surface at 620 K. Above 640 K, the SiH surface species decreased concurrently with H 2 desorption. Adsorption studies were also conducted at various isothermal temperatures. These disilane adsorption and decomposition experiments provide important insights to the surface chemistry during silicon CVD and ALE processing.

Degenerate deformations and uniqueness in highly elastic networks

This work deals with the continuum theory for plane deformations of a network formed of two families of highly elastic cords, under the assumption of no resistance to shearing. Following Pipkin [3] it is shown that there exists a collapse mode of deformation in which a finite region of the network collapses onto a single curve and examples are exhibited which correspond to a universal deformation and to a universal state of tension. It is further shown that the assumption that the cords can withstand no compression leads to the existence of half-slack and fully-slack regions, as defined by Pipkin [5]. The most general deformation associated with a half-slack region is determined. A variational principle is established for the general boundary value problem and it is shown that, for strain-energy functions which are quadratic in the stretches of the cords, this leads to a minimum principle and a generalized uniqueness theorem. A stability and uniqueness theorem is derived for the materials with a more general strain energy function.

New aspects of the decomposition kinetics of calcite: Part 1. Isothermal decomposition

Under experimental conditions which tend to minimise the effects of heat and mass transfer, the kinetics of the decomposition of calcite according to CaCO 3(s) CaO(s) + CO 2(g) is split by the restriction of CO 2 transport at the degree of conversion α t when the channels in the CaO(s) surrounding the reactant provide the only diffusion path. Because of the resulting convective cooling beyond α t, the phase boundary reaction proceeds initially with the reaction-only activation energy E a(1) = 192.89 kJ mol −1 up to α t, after which the reaction proceeds with an apparent activation energy of E a(2) = 210.33kJ mol −1. The diffusion-controlled reaction proceeds with the mean value of the activation energy E a(D 1) = 0.5 ( E a(1) + E a(2)) = 201.65 kJ mol −1. The activation energies differ by the same amount, i.e. E a(D 1) − E a(1) = E a(2) − E a(D 1) = 8.72 kJ mol −1, equivalent to the degenerate deformation vibration v 4 = δ(O-C-O) of calcite observed at 706 cm −1 (infrared) and 714 cm −1 (Raman), which for a transition state sensitive to the instantaneous transport of CO 2, complements the cage effect exercised by the lattice, thus giving strong evidence supporting our mechanistic interpretation of the decomposition kinetics.

Local ordering in the disordered phases I and II of NH4Cl and NH4Br

A complete infrared study of NH4Cl and NH4Br has been carried out and new results are reported for the two disordered phases I and II. The study includes measurements and interpretations of the IR spectral bands, band width, intensities and frequencies of the internal modes as functions of temperatures. Special attention is paid to the doubly degenerate symmetric deformation mode ν2 and to the triply degenerate asymmetric deformation modeν 4. For both of the two ammonium halides, the disordering inherent in these two phases generates spectral anomalies. The results reveal the presence of local ordering accompanying the disordering. The energy required for orientation of NH 4 + ion is calculated to be 0.52 eV (for NH4Cl) and 0.48 eV (for NH4Br).

Microwave spectrum, structure, quadrupole coupling constants, and dipole moment of bromotrifluorosilane

The microwave spectra of four isotopic species of bromotrifluorosilane, 28SiF 3 79Br, 28SiF 3 81Br, 30SiF 3 79Br, and 30SiF 3 81Br, have been measured. Analysis of the two main species has led to considerable refinement of earlier published constants. Rotational constants for 28SiF 3 79Br are B 0 0 = 1550.060(1) MHz, D J = 0.166(4) kHz, and D JK = 1.245(9) kHz. The nuclear quadrupole coupling constants arising from 79Br and 81Br were revised to 344.0(1) and 287.4(1) MHz, respectively. The average zero-point structure has been determined as SiB = 2.1559 ±0.0037 A ̊ , , SiF= 1.5591±0.0052 A ̊ FSiBr = 110.38±0.19 °, , FSiF= 108.55±0.19 °. The dipole moment was determined, taking full account of Stark-quadrupole interaction, to be μ = 0.835(7) D. Two vibrational satellite series have also been analyzed. The most prominent series arises from a degenerate vibration at about 230 cm −1 with q 6 = 1.17 and α 6 = 1.19 MHz. The second series is derived from the degenerate asymmetric deformation of the SiF 3 top at about 380 cm −1 with q 5 = 0.31 and α 5 = −1.31 MHz.

CO 2 laser Stark spectroscopy of the Coriolis-coupled ν2 and ν5 bands of CD 3Br

The ν 2 (CD 3 symmetrical deformation) and ν 5 (CD 3 degenerate deformation) fundamental bands of CD 3Br were studied by 9.4- and 10.4-μm CO 2 laser Stark spectroscopy. Stark resonances originating from 28 and 53 rovibrational transitions of the ν 2 and ν 5 bands, respectively, were assigned for each of the isotopic species, CD 3 79Br and CD 3 81Br. These two bands were simultaneously analyzed with explicit inclusion of the ν 2- ν 5 Coriolis interaction, yielding precise molecular constants in the ν 2 and ν 5 excited states as well as the Coriolis coupling constant. The molecular constants obtained are consistent between the two isotopic species and are in good agreement with the results of high-resolution infrared studies. The band origins and dipole moments are CD 3 79Br CD 3 81Br ν 2 991.396 82 (18) 991.388 46 (17) cm −1 ν 5 1055.469 00 (12) 1055.466 32 (12) cm −1 μ 0 1.830 42 (52) 1.829 84 (47) D μ 2 1.829 93 (48) 1.829 57 (46) D μ 5 1.832 23 (60) 1.831 19 (56) D where the figures in parentheses are three times the standard deviations in the least-squares fit.