Orbit Branching Research Articles

Anatomic and Embryologic Analysis of the Dural Branches of the Ophthalmic Artery.

The ophthalmic artery has one of the most fascinating embryologic developments among the craniofacial arteries. Most of the ophthalmic artery orbital branches develop from the formation and regression of the stapedial artery and share their origin with dural branches of the ophthalmic artery. The concomitant embryologic development of the ophthalmic artery and middle meningeal artery explains adequately the important varieties of anastomosis between these 2 arteries. It also explains the presence of many dural branches from the ophthalmic artery. In this review, we focused on dural branches of the ophthalmic artery with the description of rare variations possible, in particular the ophthalmic artery origin of the middle meningeal artery and the ophthalmic artery origin of the marginal tentorial artery.

Retinal Vasculature Changes after Bypass Surgery for Moyamoya Disease

A 48-year-old woman with slurred speech was diagnosed with Moyamoya disease. Digital subtraction angiography disclosed left ophthalmic artery originating from the internal carotid artery (Fig A, arrow), and supplied by orbital branches of the middle meningeal and facial artery (Fig A, arrowhead). Preoperative examinations showed normal superficial vascular complex (SVC) in the left eye (OS) on OCT angiography (Fig B). She underwent left extracranial-intracranial bypass from the superficial temporal artery to the middle cerebral artery.

State-to-state predissociation dynamics of hydroxyl radical via the A2Σ+ state

ABSTRACT Photo-predissociation dynamics of jet-cooled hydroxyl radical (OH) via several rovibrational levels (v′ = 2–4, N′ = 0–2, J′ = 0.5–2.5, F 1) in the A2Σ+ state are studied using the high–n Rydberg-atom time-of-flight (HRTOF) technique. Spin–orbit branching fractions and angular distributions of the H(2S) + O(3PJ = 2,1,0) product channels are measured in the product translational energy distributions. The A2Σ+ v′ = 2 and 3 states of OH predissociate predominantly via the single 14Σ− repulsive state, while the A2Σ+ v′ = 4 state predissociates via the 14Σ−, 12Σ−, and 14Π repulsive states and quantum interferences among these dissociation pathways play an important role in the O(3PJ = 2,1,0) product fine-structure state distribution. The experimental O(3PJ) product spin–orbit branching ratios are in excellent agreement with the full quantum multichannel scattering calculations that include all the interactions in the crossing region, recoupling zone, and asymptotic zone [Parlant and Yarkony, J. Chem. Phys. 110, 363 (1999)]. The product angular distributions strongly depend on the rotational transitions and rotational levels in the A2Σ+ state. The measured anisotropy parameters are in reasonable agreement with predictions from the simulation programme (Betaofnu) [Kim et al., J. Chem. Phys. 125, 133316 (2006)], using dissociation lifetime, excitation frequency, rotational level, and rotational constant. The predissociation time scales of OH A2Σ+ are determined to be 130 ± 30 ns and ≥ 14 ± 3 ps for the v′ = 2, N′ = 2, J′ = 2.5 and v′ = 4, N′ = 0, J′ = 0.5 levels, respectively.

Natural Orbital Branching Scheme for Time-Dependent Density Functional Theory Nonadiabatic Simulations.

Real time-time-dependent density functional theory (rt-TDDFT) has now been used to study a wide range of problems, from optical excitation to charge transfer, to ion collision, and to ultrafast phase transition. However, conventional rt-TDDFT Ehrenfest dynamics for nuclear movement lacks a few critical features to describe many problems: the detail balance between state transitions, decoherence for the wave function evolution, and stochastic branching of the nuclear trajectory. There are many-body formalisms to describe such nonadiabatic molecular dynamics, especially the ones based on mixed quantum/classical simulations, like the surface hopping and wave function collapsing schemes. However, there are still challenges to implement such many-body formalisms to the rt-TDDFT simulations, especially for large systems where the excited state electronic structure configuration space is large. Here we introduce two new algorithms for nonadiabatic rt-TDDFT simulations: the first is a Boltzmann factor algorithm which introduces decoherence and detailed balance in the carrier dynamics but uses mean field theory for nuclear trajectory. The second is a natural orbital branching (NOB) formalism, which uses a time-dependent density matrix for electron evolution and a natural orbital set to collapse the wave function upon. It provides the features of decoherence, detailed balance, and trajectory branching. We have tested these methods for a molecule radiolysis decay problem. We found that these methods can be used to study such radiolysis problems in which the molecule is broken into many fragments following complex electronic structure transition paths. The computational time of NOB is similar to that of the original plain rt-TDDFT simulations.

Guaranteed Estimates for the Length of Branches of Periodic Orbits for Equivariant Hopf Bifurcation

Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the assumption that the nonlinear terms satisfy a linear estimate in a ball. If the estimate is global, then the branch is unbounded. The results are formulated in an equivariant setting where the system can have multiple branches of periodic orbits characterized by different groups of symmetries. The nonlocal analysis is based on the equivariant degree method, which allows us to handle both generic and degenerate Hopf bifurcations. This is illustrated by examples.

Stapedial Artery: From Embryology to Different Possible Adult Configurations.

The stapedial artery is an embryonic artery that represents the precursor of some orbital, dural, and maxillary branches. Although its embryologic development and transformations are very complex, it is mandatory to understand the numerous anatomic variations of the middle meningeal artery. Thus, in the first part of this review, we describe in detail the hyostapedial system development with its variants, referring also to some critical points of ICA, ophthalmic artery, trigeminal artery, and inferolateral trunk embryology. This basis will allow the understanding of the anatomic variants of the middle meningeal artery, which we address in the second part of the review.

Dissipative generation of steady-state entanglement of two separated SiV$$^{-}$$ centers coupled to photonic crystal cavities

We propose an efficient scheme for the dissipative generation of steady-state entanglement of two negatively charged silicon-vacancy (SiV $$^{-}$$ ) centers, which are coupled to two separated photonic crystal cavities, respectively. With the external driving fields to tailor the desired interaction between the Zeeman-split lower orbital branches of the ground states of the SiV $$^{-}$$ centers and the cavity fields, we show that the heavily damped cavities can induce an effective quantum reservoir coupled to the two SiV $$^{-}$$ centers. Based on a form of quantum reservoir engineering, the two SiV $$^{-}$$ centers can be cooled down to an entangled state at stationary state. Our scheme has the distinct feature that the decay of the cavities as resource is utilized for producing the steady-state entanglement, which does not need to exactly prepare the initial state of the system. The present work may open up promising perspectives for realizing quantum networks and quantum information processing with solid-state SiV $$^{-}$$ centers in nanophotonic structures.

Correlations of the parameters of cardiopulmonary bypass and hemodynamics during cardiac surgery and the structural and functional state of the retina

Objective. To study the structural and functional retinal changes developed in cardiac surgery patients as a consequence of cardiopulmonary bypass and to identify the factors aff ecting the nature and extent of changes observed.Material and Methods. Ten patients who underwent cardiac surgery under cardiopulmonary bypass (CPB) were studied. The ophthalmologic examination was performed before cardiac surgery and 10–14 days after the surgery.Results. On days 10 to 14, after cardiac surgery, visual acuity was restored to the maximum; the perimetry indicators, the level of intraocular pressure, and the structures of the anterior segment of the eyeballs did not change signifi cantly. The ophthalmoscopy revealed the foci of ischemic edema in the fundus along with the fi rst- and second-order arteries in 30% of cases. The thickness of ganglionic and nerve fi ber layers decreased in one patient (10%), which may be associated with the intraoperative ischemia of orbital artery branches feeding the optic nerve. These changes had direct relationships with the level of maximum mean blood pressure (MBP) during CPB and the fl uctuation of absolute MBP values during CPB: MBP ≥ 90 mmHg during CPB was associated with the occurrence of ischemic foci in the retina in 100% of cases. If the diff erence between the maximum and minimum MBP levels during CPB exceeded 20 mmHg, the changes in the retina occurred more frequently (p = 0.0350) than in the cases where MBP fl uctuations during CPB were less than 20 mmHg.Conclusions. The most signifi cant changes in the vision organs of patients undergoing cardiac surgery under CPB occur in the retina. Factors associated with the occurrence of pathological ischemic changes in the retina were fl uctuations in MBP during CPB (≥20 mmHg) and the absolute value of maximum MBP during CPB (>90 mmHg).

Large oscillation of electrostatically actuated curved beams

This paper investigates the responses of initially curved micro-beams subjected to an electrostatic excitation. A Euler–Bernoulli beam theory is utilized to derive the governing equation of motion. A reduced-order model was developed by discretizing the equation of motion using straight beam mode shapes as basis functions in a Galerkin expansion. The results show evidence of the superharmonic resonances of order-three and two in addition to primary resonance. The co-existence of multiple stable orbits observed around only one stable equilibrium and under excitation waveforms with RMS voltage less than the snap-back voltage. These branches are a branch of small orbits within a narrow potential well and two branches of medium-sized and large orbits within a wider potential well. The transition between them results in the characteristic of the double peaks appearing in the frequency-response curve. We also report a bubble structure along the medium-sized branch consists of a cascade of period-doubling bifurcations and a cascade of reverse period-doubling bifurcations. A chaotic attractor develops within that structure at larger excitation levels. It demonstrates evidence of chaos with a wide-based spectrum and an elevated noise-floor. Odd-periodic windows appear also within the attractor including period-three (P-3), period-five (P-5) and period-six (P-6) windows. The chaotic attractor terminates in a cascade of reverse period-doubling bifurcations of period-four (P-4) orbits and period-two (P-2) orbits.

The hidden unstable orbits of maps with gaps

Piecewise-continuous maps consist of smooth bran- ches separated by jumps, i.e. isolated discontinui- ties. They appear not to be constrained by the same rules that come with being continuous or differentiable, able to exhibit period incrementing and period adding bifurcations in which branches of attractors seem to appear ‘out of nowhere’, and able to break the rule that ‘period three implies chaos’. We will show here that piecewise maps are not actually so free of the rules governing their continuous cousins, once they are recognized as containing numerous unstable orbits that can only be found by explicitly including the ‘gap’ in the map’s definition. The addition of these ‘hidden’ orbits—which possess an iterate that lies on the discontinuity—bring the theory of piecewise-continuous maps closer to continuous maps. They restore the connections between branches of stable periodic orbits that are missing if the gap is not fully accounted for, showing that stability changes must occur in discontinuous maps via stability changes not so different to smooth maps, and bringing piecewise maps back under the powerful umbrella of Sharkovskii’s theorem. Hidden orbits are also vital for understanding what happens if the discontinuity is smoothed out to render the map continuous and/or differentiable.

Resonance enhanced multiphoton ionisation (REMPI) detection of Cl(2Pj) atom in the photodissociation of halogenated pyrimidines at 235 nm: role of triplet states

ABSTRACTThe dynamics of chlorine atom (2Pj) formation in the photodissociation process of halogen substituted pyrimidines, namely, 2,4,6-trichloropyrimidine and 5-chloro-2,4,6-trifluoropyrimidine have been studied around 235 nm using Resonance Enhanced Multiphoton Ionisation Time-of-Flight Mass Spectrometry technique. For the chlorine atom dissociation channel, we have determined the translational energy distribution, the recoil anisotropy parameter, β, and the spin–orbit branching ratio. In both the molecules, the TOF profiles for Cl (2P3/2) and Cl* (2P1/2) are found to be independent of laser polarisation suggesting a zero value for β, within the experimental uncertainties. For 2,4,6-trichloropyrimidine, the average translational energies for Cl and Cl* elimination channels are determined to be 6.0 ± 1.2 and 7.0 ± 1.5 kcal/mol, respectively. Similarly, for 5-chloro-2,4,6-trifluoropyrimidine, the average translational energies for Cl and Cl* elimination channels are determined to be 6.5 ± 1.2 and 7.9 ± 1.6 kcal/mol, respectively. Computational calculations are performed to generate the potential energy curves along the dissociating C-Cl bond using equation of motion coupled cluster with single and double excitations (EOM-CCSD) method. Computational studies suggest the role of triplet states in the photodissociation process forming the Cl atom.

A computational comparison of symmetry handling methods for mixed integer programs

The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received significant attention, both in theory and practice. This paper compares different methods for handling symmetries using a common implementation framework. We start by investigating the computation of symmetries and analyze the symmetries present in the MIPLIB 2010 instances. It turns out that many instances are affected by symmetry and most symmetry groups contain full symmetric groups as factors. We then present (variants of) six symmetry handling methods from the literature. Their implementation is tested on several testsets. On very symmetric instances used previously in the literature, it is essential to use methods like isomorphism pruning, orbital fixing, or orbital branching. Moreover, tests on the MIPLIB instances show that isomorphism pruning, orbital fixing, or adding symmetry breaking inequalities allow to speed-up the solution process by about 15% and more instances can be solved within the time limit.

Orbital State Manipulation of a Diamond Nitrogen-Vacancy Center Using a Mechanical Resonator.

We study the resonant optical transitions of a single nitrogen-vacancy (NV) center that is coherently dressed by a strong mechanical drive. Using a gigahertz-frequency diamond mechanical resonator that is strain coupled to a NV center's orbital states, we demonstrate coherent Raman sidebands out to the ninth order and orbital-phonon interactions that mix the two excited-state orbital branches. These interactions are spectroscopically revealed through a multiphonon Rabi splitting of the orbital branches which scales as a function of resonator driving amplitude and is successfully reproduced in a quantum model. Finally, we discuss the application of mechanical driving to engineering NV-center orbital states.

Nonlinear modes of large-amplitude ship motion with roll-pitch coupling

This research pertains to the dynamics of a ship taking into account the nonlinear coupling of roll and pitch degrees of freedom. Such nonlinearity has critical implications for large-amplitude ship motion, and can thus be useful in understanding conditions leading to capsize. The nonlinear normal modes of the conservative system are determined numerically and are displayed in a frequency-energy plot, which clarifies the bifurcations that connect the various branches of periodic orbits. Numerical simulations show that, although the solutions on most branches result in capsize if their energy is beyond a common critical value, a few branches contain stable solutions at higher energies that do not lead to capsize, suggesting possible methods of capsize mitigation. We study a class of solutions analytically using a complexification-averaging technique. Finally, we run a simulation in the case of light damping in roll with high-energy initial conditions, illustrating transitions between branches that occur in the direction of decreasing energy on the frequency-energy plot.

Nonlinear modes of large-amplitude ship motion with roll-pitch coupling

This research pertains to the dynamics of a ship taking into account the nonlinear coupling of roll and pitch degrees of freedom. Such nonlinearity has critical implications for large-amplitude ship motion, and can thus be useful in understanding conditions leading to capsize. The nonlinear normal modes of the conservative system are determined numerically and are displayed in a frequency-energy plot, which clarifies the bifurcations that connect the various branches of periodic orbits. Numerical simulations show that, although the solutions on most branches result in capsize if their energy is beyond a common critical value, a few branches contain stable solutions at higher energies that do not lead to capsize, suggesting possible methods of capsize mitigation. We study a class of solutions analytically using a complexification-averaging technique. Finally, we run a simulation in the case of light damping in roll with high-energy initial conditions, illustrating transitions between branches that occur in the direction of decreasing energy on the frequency-energy plot.

Periodic Oscillations and Waves in Nonlinear Weakly Coupled Dispersive Systems

Bifurcations of periodic solutions in autonomous nonlinear systems of weakly coupled equations are studied. A comparative analysis is carried out between the mechanisms of Lyapunov–Schmidt reduction of bifurcation equations for solutions close to harmonic oscillations and cnoidal waves. Sufficient conditions for the branching of orbits of solutions are formulated in terms of the Pontryagin functional depending on perturbing terms.

Coherent control of the silicon-vacancy spin in diamond

Spin impurities in diamond have emerged as a promising building block in a wide range of solid-state-based quantum technologies. The negatively charged silicon-vacancy centre combines the advantages of its high-quality photonic properties with a ground-state electronic spin, which can be read out optically. However, for this spin to be operational as a quantum bit, full quantum control is essential. Here we report the measurement of optically detected magnetic resonance and the demonstration of coherent control of a single silicon-vacancy centre spin with a microwave field. Using Ramsey interferometry, we directly measure a spin coherence time, T2*, of 115±9 ns at 3.6 K. The temperature dependence of coherence times indicates that dephasing and decay of the spin arise from single-phonon-mediated excitation between orbital branches of the ground state. Our results enable the silicon-vacancy centre spin to become a controllable resource to establish spin-photon quantum interfaces.

Do Trigeminal Nerves that Innervate the Nose and External Nares Project to Medullary Dorsal Horn Locations Activated during Voluntary Diving in Rats?

Underwater diving initiates the diving response, an autonomic cardiorespiratory reflex that includes parasympathetically‐mediated bradycardia, a sympathetically‐mediated increase in total peripheral resistance, and apnea. The initial afferent node of the reflex circuitry includes the ventral tip of the medullary dorsal horn (MDH), between the pyramidal decussation and obex. This region is also the location of the central terminations of trigeminal nerves that innervate the nose and external nares. Accordingly, the objective of this research was to compare the pattern of neuronal activation of secondary neurons activated by voluntary diving, as determined by neuronal Fos production, with the central terminations of specific trigeminal nerves that innervate the nose and external nares, as determined by the transganglionic tracer Wheat Germ Agglutinin (WGA). Sprague‐Dawley rats (N=12) were trained to voluntarily dive through a 5 m underwater maze. Six rats then received bilateral AEN sectioning, while 6 rats received sham surgery. Nine days post‐surgery all rats had 24 dive trials over 2 hours to activate brainstem neurons to produce Fos. Other rats had 1 μl of 100% WGA injected into the anterior ethmoidal nerve (AEN; N=4), the main orbital branch of the infraorbital nerve (ION; N=7), terminal branches of the ION that innervate the nasal region (N=9), or supratrochlear nerve (N=8). Results indicate Fos was primarily located within the ventral tip of the superficial MDH and adjacent paratrigeminal nucleus, between the pyramidal decussation caudally and the obex rostrally. The Fos labeling was heaviest when the area postrema was present, especially when Spinal Trigeminal Nucleus Interpolaris displaces the ventral MDH medially. This pattern of Fos labeling within the MDH was similar in rats both with and without intact AENs. Within the MDH WGA central termination sites showed varying degrees of overlap with the location of Fos‐positive neurons. The AEN WGA labeling had the best overlap with Fos‐positive neurons. The main orbital branch of the ION had extensive WGA labeling throughout the MDH, both ventrally and dorsally, and did partially overlap the MDH Fos labeling. The WGA labeling from both nasal branches of the ION and supratrochlear nerve were located more caudally within the MDH near the pyramidal decussation, thus showing poor overlap with the Fos labeling. We conclude that the AEN, and possibly the ION, provides the anatomical pathway that provides the afferent information necessary to initiate the mammalian diving response. However, in the absence of the AEN, it is not clear whether the ION can actually provide this afferent information.Support or Funding InformationSupported by MWU Intramural funding (PFM), CCOM Suarez Summer Research Fellowships (BDP and KAL), and CHS MBS program (EAW).

A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE

In this paper, a method for computing periodic orbits of the Kuramoto--Sivashinsky PDE via rigorous numerics is presented. This is an application and an implementation of the theoretical method introduced in [J.-L. Figueras, M. Gameiro, J.-P. Lessard, and R. de la Llave, “A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations,” SIAM J. Appl. Dyn. Syst., to appear]. Using a Newton--Kantorovich-type argument (the radii polynomial approach), existence of solutions is obtained in a weighted $\ell^\infty$ Banach space of Fourier coefficients. Once a proof of a periodic orbit is done, an associated eigenvalue problem is solved and Floquet exponents are rigorously computed, yielding proofs that some periodic orbits are unstable. Finally, a predictor-corrector continuation method is introduced to rigorously compute global smooth branches of periodic orbits. An alternative approach and independent implementation of [J.-L. Figueras, M. Gameiro, J.-P. Less...

Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori

We present a concurrent algorithm for rigorous validation of the existence of continuous branches of stable elliptic fixed points for area-preserving planar maps. The method utilizes a classical theorem of Siegel and Moser combined with computed-assisted estimation of higher order derivatives of maps, continuation along the parameter range, and concurrent scheduling of tasks. We apply the algorithm to certain exemplary Poincare maps coming from reversible or Hamiltonian systems: the periodically forced pendulum equations, the Michelson system, and the Henon--Heiles Hamiltonian. Moreover, our algorithm provides at once a computer-assisted proof of the existence of wide branches of stable elliptic periodic solutions and the existence of invariant tori surrounding them.