Tunneling Trajectories Research Articles

Dendritic-Acidizing Update: The Light at the End of the Tunnel

Summary In this paper, we provide an update on recent advances for and summarize global experiences with dendritic-acidizing (DA) methods, or acid tunneling. We include both coiled-tubing (CT) deployed methods and non-CT methods, and discuss process limitations, candidate-selection criteria, job-design factors, operational learnings, risks, and surveillance requirements and opportunities. A comprehensive review of published information is provided for three different tunneling methods along with relevant information for several other tunneling methods. This literature information is supplemented by depth, temperature, and pressure records for the three processes, which are discussed in detail. Execution factors such as logistics required, length of time required, and volumes of acid and other fluids used are also compared for the three methods. Previous papers have focused on only one of the methods, whereas we will discuss acid-job optimization, process risks, and surveillance requirements for multiple acid-tunneling methods in substantially greater depth than have past authors. The three methods detailed in this paper are all viable but may have different niches. Differences in the job counts for the different methods are easily explained by differences in process vintages, execution speeds, and depth limitations. Previous optimization efforts were focused on tunnel creation but not acid-job effectiveness in terms of the wormholes generated adjacent to the tunnels; however, some progress is now being made in that regard. There are differences in the processes regarding pushing or pulling the jetting nozzles into the tunnels, and differences in resulting tunnel trajectories. Prejob caliper data are more critical for one of the processes than for the others, and there are significant differences in ability to measure or control tunnel direction. The tunneling tools have different sizes, but when tool-size alternatives are available, the larger tool sizes offer no clear advantages to the operator. Useful risk-mitigation measures are also discussed, and a comprehensive bibliography is included to facilitate further examination of the technology alternatives by other petroleum-industry professionals.

Experimental investigation of the time-dependent response of unreinforced and reinforced tunnel faces in cohesive soils

In spite of the increasing diffusion of tunnel boring machines, conventional tunnelling is still preferred for economic reasons in case of short tunnels, unconventional cross sections or irregular tunnel trajectories. In conventional tunnelling, the mechanical response of the tunnel front is a main concern and, when tunnels are excavated in cohesive soils, this is dominated by the time factor, related to geometry, to the mean excavation rate and to the hydro-mechanical properties of the materials involved. This is particularly evident during excavation standstill: front displacements progressively increase with time and, in many cases, the system response under long-term conditions becomes unstable. In conventional tunnelling, a common technique employed to improve the system response (under both short- and long-term conditions) is the installation of fibreglass tubes within the advance core. In this paper, the mechanical response of both unreinforced and reinforced deep tunnel fronts in cohesive soils is experimentally analysed. In particular, the results of a series of 1 g small-scale tests, taking into account both the influence of the excavation rate (the unloading time) on the system response and the evolution with time of the tunnel face displacements, induced by a rapid reduction in the horizontal stress applied on the tunnel face, are reported.

Progress in study of low-energy photoelectron in ultra-fast strong fields-analytical R-matrix theory based semiclassical trajectory method

The semi-classical method based on the recently developed analytical R-matrix theory is reviewed in this work. The method is described with the application to ultra-fast strong-field direct ionization of atoms with one active electron in a linearly polarized field[Torlina L, Smirnova O 2012 Phys. Rev. A 86 043408]. The analytical R-matrix theory separates the space into inner and outer regions, naturally allowing the possibility of an analytical or semi-analytical description of wave function in the outer region, which can be approximated by Eikonal-Volkov solutions while the inner region provides well-defined boundary conditions. Applying the stationary phase method, the calculation of the ionization amplitude is cast into a superposition of components from trajectories and their associated phase factors. The shape of the tunneling wave packets associated with different instants of ionization is presented. It shows the exponential cost of deviating from the optimal tunneling trajectory renders the tunneling wave packet a Gaussian shape surrounding the semi-classical trajectory. The intrinsically non-adiabatic corrections to the sub-cycle ionization amplitude in the presence of both the Coulomb potential and the laser field is shown to have different influences on the probability of ionization. As a specific study case, soft recollisions of the released electron near the ionic core is investigated by using pure light-driven trajectories with Coulomb-corrected phase factor[Pisanty E, Ivanov M 2016 Phys. Rev. A 93 043408]. Incorporating the Coulomb potential, it is found problematic to use the conventional integration contour as chosen in other methods with trajectory-based Coulomb corrections, because the integration contour may run into the Coulomb-induced branch cuts and hence the analyticity of the integrand fails. In order to overcome the problem, the evolution time of the post-tunneling electron is extended into the complex domain which allows a trajectory to have an imaginary component. As the soft recollision occurs, the calculation of the ionization amplitude requires navigating the branch cuts cautiously. The navigating scheme is found based on closest-approach times which are the roots of closest-approach times equations. The appropriately selected closest-approach times that always present in the middle of branch-cut gate may serve to circumvent these branch cuts. The distribution of the closest-approach times presents rich geometrical structures in both the classical and quantum domains, and intriguing features of complex trajectories emerge as the electron returns near the core. Soft recollisions responsible for the low-energy structures are embedded in the geometry, and the underlying emergence of near-zero energy structures is discussed with the prediction of possible observations in experiments.

Time dependent semiclassical tunneling through one dimensional barriers using only real valued trajectories.

The time independent semiclassical treatment of barrier tunneling has been understood for a very long time. Several semiclassical approaches to time dependent tunneling through barriers have also been presented. These typically involve trajectories for which the position variable is a complex function of time. In this paper, a method is presented that uses only real valued trajectories, thus avoiding the complications that can arise when complex trajectories are employed. This is accomplished by expressing the time dependent wave packet as an integration over momentum. The action function in the exponent in this expression is expanded to second order in the momentum. The expansion is around the momentum, p0(*) , at which the derivative of the real part of the action is zero. The resulting Gaussian integral is then taken. The stationary phase approximation requires that the derivative of the full action is zero at the expansion point, and this leads to a complex initial momentum and complex tunneling trajectories. The "pseudo-stationary phase" approximation employed in this work results in real values for the initial momentum and real valued trajectories. The transmission probabilities obtained are found to be in good agreement with exact quantum results.

Part II: The 50°/60° fibular tunnel trajectory for posterolateral corner reconstruction in a cadaver model.

Using data from our MRI study, we found that a tunnel oriented 50° externally rotated and 60° cephalad would better connect the fibular collateral ligament (FCL) insertion to the popliteofibular ligament (PFL) insertion as compared to a traditional anterior-to-posterior (A-P) fibular tunnel. The purpose of this study was to test that finding in a cadaver model. In eight cadaver knee pairs (16 knees), a guide pin was driven from the fibular FCL insertion point in a 50° externally rotated and 60° cephalad trajectory in 8 knees, and in a traditional A-P trajectory in the contralateral 8 knees. Proximity of the pin to the native PFL insertion, the peroneal and tibial nerves was measured, followed by drilling over the guide pin and measuring the remaining fibular bone stock. In comparison with the A-P fibular tunnel technique, the 50°/60° technique resulted in a fibular exit point significantly closer to the native PFL insertion (p < 0.01). Both techniques were safe with regard to the tibial and peroneal nerves. There were no instances of fibular wall blowout in either technique; however, there was less superior bone remaining in the 50°/60° technique (p < 0.04). In a cadaveric model, the 50°/60° technique for PLC reconstruction resulted in a more anatomic-based tunnel than an A-P fibular tunnel.

A Rare Technical Complication Causing ACL Graft Failure: Aberrant Femoral Tunnel Trajectory and Posterolateral Corner Compromise: A Case Report.

In order to o reproduce normal joint kinematics of the knee following anterior cruciate ligament (ACL) injury, anatomic reconstruction has been advocated1-6. This can be achieved best by recreating the native ACL footprints. Matching the location of the intra-articular apertures of the femoral and tibial tunnels to the anatomic footprints of the native ACL has been reported to be accomplished most accurately with techniques other than traditional transtibial drilling7-11. In the pediatric population, the trajectory of the femoral tunnel is more heavily scrutinized because of its relationship to the distal femoral physis. However, in adults, clinical evidence is sparse regarding the appropriate tunnel trajectory. Cadaveric studies detailing the anatomic relationships of the femoral tunnel to the structures of the lateral aspect of the knee also have been reported12-16. The proximity of the lateral exit point of the femoral tunnel to critical lateral structures placed with an independent tunnel drilling technique has been shown to be a potential source of iatrogenic injury15. To our knowledge, there are no reports in the literature of injury to the posterolateral corner (PLC) as a result of femoral tunnel placement in ACL reconstruction. We present a case of PLC compromise and ACL graft failure following aberrant femoral tunnel placement in a revision ACL reconstruction. The patient was informed that data concerning the case would be submitted for publication, and he provided consent. A twenty-one-year-old male intercollegiate football player presented after sustaining a knee injury while performing a lateral shuffling drill during an off-season workout. He had been treated by two different orthopaedists and had undergone two surgeries on the affected knee for treatment of ACL insufficiency prior to this most recent injury. Three years prior to presentation, he had ruptured his …

Magnetoresistance of an Anderson Insulator of Bosons

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunneling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ(-1)(B)-ξ(-1)(0)~B(4/5). The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the nontrivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.

Dynamical tunneling-like effects in 1D classical systems

Dynamical tunneling occurs when a particle tunnels between two distinct classically trapped periodic regions of classical phase space that are not separated by a potential barrier. Although the dynamical tunneling has been observed in many multi-dimensional Hamiltonian systems, it has not been observed in 1D systems described by a single potential. In this paper, we show that classical trajectories of real potentials such as V1(x) = x4 exhibit dynamical tunneling-like behavior when energy or time is complex. It was found that the doubly periodic nature of the Jacobian elliptic functions is responsible for this dynamical tunneling-like behavior. The time spent in one region by the tunneling trajectory before crossing over to the other is found to be proportional to , where total energy E = E0 + iΔE with E0 < 0. Furthermore, we demonstrate that classical trajectories of the non-Hermitian system V2(x) = x4 + (1 + i)x show evidence of dynamical tunneling even for real energies. The role of complex time in dynamical tunneling is discussed.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

Anatomic relationships of single-incision midurethral slings

The objective of the study was to evaluate the anatomic relationships of anchor points of single-incision midurethral slings with 2 common placement trajectories. In 30 female pelvic halves, a probe was introduced through a suburethral tunnel following 45° and 90° angle trajectories. The corresponding anchor points were tagged. Distances to the obturator canal, accessory obturator vessels, dorsal vein of clitoris, and external iliac vein were recorded. Both suburethral tunnel trajectories and their respective anchor points remained caudad to the obturator internus muscle in 100% of dissections. The closest distance between either anchor point to the obturator canal was 1.6 cm. The closest distance from the 45° and 90° anchor points to the accessory obturator vessels was 1.6 and 1.5 cm, respectively. The anchor points of single-incision midurethral slings are in close proximity to vascular structures that could be injured with inadvertent entry into the retropubic space.

Driving force planning in shield tunneling based on Markov decision processes

In shield tunneling, the control system needs very reliable capability of deviation rectifying in order to ensure that the tunnel trajectory meets the permissible criterion. To this goal, we present an approach that adopts Markov decision process (MDP) theory to plan the driving force with explicit representation of the uncertainty during excavation. The shield attitudes of possible world and driving forces during excavation are scattered as a state set and an action set, respectively. In particular, an evaluation function is proposed with consideration of the stability of driving force and the deviation of shield attitude. Unlike the deterministic approach, the driving forces based on MDP model lead to an uncertain effect and the attitude is known only with an imprecise probability. We consider the case that the transition probability varies in a given domain estimated by field data, and discuss the optimal policy based on the interval arithmetic. The validity of the approach is discussed by comparing the driving force planning with the actual operating data from the field records of Line 9 in Tianjin. It is proved that the MDP model is reasonable enough to predict the driving force for automatic deviation rectifying.

Reversible rock-slope deformations caused by cyclic water-table fluctuations in mountain slopes of the Central Alps, Switzerland

Within the framework of the Gotthard Base Tunnel Project in the Central Alps, Switzerland, geodetic monitoring networks were installed above the tunnel trajectory in alpine valleys. Natural ground-surface deformation recorded in the years prior to the tunneling excavation was seen to contain an unexpectedly large cyclical component of horizontal strain across the valleys, which was seasonal and appeared to be due to elastic processes. The strain is strongly correlated with snow melt and rainstorm precipitation, suggesting the implied rock-mass deformation is driven by changes in water-table elevation within adjacent mountain slopes. The horizontal strains are of the order of 1–2 · 10–5, which is close to the design limits that can be accommodated by hydropower arch dams in the study area. This study investigates these processes in detail and describes a new mathematical model (REROD), which is able to accurately reproduce and predict such natural rock-slope displacements. The model implements a transfer-function approach to predict the valley-crossing strains from rainfall and winter snow height data recorded at nearby meteorological stations. It has been used to estimate and remove the natural strain signal from the net recorded deformation so as to resolve the component due to tunneling.

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by Hislop and Sigal (1989 Mem. AMS 78 No 399), we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e. theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short-range interactions and ‘almost’ linear in the case of long-range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.

Conifolds and tunneling in the string landscape

We investigate flux vacua on a variety of one-parameter Calabi-Yau compactifications, and find many examples that are connected through continuous monodromy transformations. For these, we undertake a detailed analysis of the tunneling dynamics and find that tunneling trajectories typically graze the conifold point---particular 3-cycles are forced to contract during such vacuum transitions. Physically, these transitions arise from the competing effects of minimizing the energy for brane nucleation (facilitating a change in flux), versus the energy cost associated with dynamical changes in the periods of certain Calabi-Yau 3-cycles. We find that tunneling only occurs when warping due to back-reaction from the flux through the shrinking cycle is properly taken into account.

A novel sports ball aerodynamics analysis tool: soccer ball design

A novel soccer ball design tool involving the optimisation of the aerodynamics is developed in this paper. The design tool allows the flight of different balls with various input conditions to be compared and the behaviour of new ball designs to be assessed. The tool was developed by combining CFD results with information from wind tunnel tests, trajectory testing, and player testing. Subsequently, the results (force coefficient data) were entered into a trajectory simulation programme. Various soccer ball designs were assessed using the design tool, and several conclusions drawn regarding aerodynamic optimisation. Two kick types are studied in this paper: curling, high-spinning kicks that are typically used for free-kicks, corners and long passes, and erratic, high-velocity, low-spinning kicks that are typically used for free-kicks, and shots on goal. The key physical phenomena relevant to both kick types were identified, and related to real game situations. Curling kicks were found to experience more sw...

Local density of states in disordered two-dimensional electron gases at high magnetic field

Motivated by high-accuracy scanning tunneling spectroscopy measurements on disordered two-dimensional electron gases in strong magnetic field, we present an expression for the local density of states (LDoS) of electrons moving in a smooth arbitrary potential landscape on the scale of the magnetic length, that can be locally described up to its second derivatives. We use a technique based on coherent-state Green's functions, allowing us to treat on an equal footing confining and open quantum systems. The energy dependence of the LDoS is found to be universal in terms of local geometric properties, such as drift velocity and potential curvature. We also show that thermal effects are quite important close to saddle points, leading to an overbroadening of the tunneling trajectories.

The quantum normal form approach to reactive scattering: The cumulative reaction probability for collinear exchange reactions

The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy-atom systems such as the nitrogen-exchange reaction, the quantum normal form approach gives excellent results and has major computational benefits over full reactive scattering approaches. For light atom systems such as the hydrogen-exchange reaction however, the quantum normal approach is shown to give only poor results. This failure is attributed to the importance of tunneling trajectories in light atom reactions that are not captured by the quantum normal form as indicated by the only very slow convergence of the quantum normal form for such systems.

Stochastic tunneling for strongly non-Gaussian inflationary theories

We reconsider the dynamics of stochastic or thermal tunneling in theories like Dirac-Born-Infeld inflation that have non-minimal kinetic terms and, as a result, strongly non-Gaussian perturbations. We first describe a local description of the tunneling process which gives results consistent with the standard Hawking-Moss tunneling. This result is under perturbative control as long as the fluctuation determinant is well approximated by a one-loop integral. We then move to a global description, using the methodology of stochastic inflation and the in-in path integral formalism. This approach shows clearly that the tunneling process becomes strongly coupled whenever the sound speed of the tunneling trajectory departs sufficiently from unity. We argue that these two very different perspectives are nevertheless consistent, and may imply the existence of a simple resummation of the strongly coupled interactions of the field.

Julia sets and chaotic tunneling: I

The tunneling phenomenon in non-integrable systems is studied in the framework of complex semiclassical theory. Complex trajectories which dominate tunneling in the presence of chaos (chaotic tunneling) are investigated numerically for several quantum maps. The discovery of a characteristic structure in the initial value representation of tunneling trajectories, named the Laputa chain, is reviewed, and it is shown how trajectories starting from Laputa chains make the dominant contribution to the semiclassical calculation of the wavefunction in the chaotic regime. This supports the argument that Laputa chains play an important role in the fully complex-domain semiclassical description of chaotic tunneling. Further, numerical analysis shows that the Laputa chain has distinct asymptotic properties in the long time limit. In particular, it is shown that the imaginary action along the trajectories starting from the Laputa chain, which determines the contribution to the tunneling probability, tends to converge absolutely in the asymptotic limit. On the basis of these features, we propose an empirical definition of the Laputa chain which can provide a basis for further mathematical development. Moreover, a connection is pointed out between the asymptotic structure of Laputa chains and Julia sets manifest in asymptotic dynamics of complex maps. Based on these results, we make the conjecture that Julia sets play a fundamental role in the complex semiclassical dynamical theory of tunneling in non-integrable systems.

Signatures of unstable semiclassical trajectories in tunneling

It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we find an additional power-law dependence of the tunneling probability on the semiclassical parameter as compared to the standard case of potential tunneling. The second signature is a substantial widening of the probability distribution over final-state quantum numbers. These effects are studied using a modified semiclassical technique which incorporates stabilization of the tunneling trajectories. The technique is derived from first principles. We obtain expressions for the inclusive and exclusive tunneling probabilities in the case of unstable semiclassical trajectories. We also investigate the ‘phase transition’ between the cases of stable and unstable trajectories across certain ‘critical’ values of energy. Finally, we derive the relation between the semiclassical probabilities of tunneling from the low-lying and highly excited initial states. This puts on firm ground a conjecture made previously in the semiclassical description of collision-induced tunneling in field theory.

Quantum interference of tunnel trajectories between states of different spin length in a dimeric molecular nanomagnet

An experimental study of a ‘dimeric’ single-molecule magnet—consisting of two coupled half-wheels of spin 7/2 each—provides evidence for quantum interference between the two sub-systems. Tunable electron spins in solid media are among the most promising candidates for qubits1. In this context, molecular nanomagnets have been proposed as hardware for quantum computation2. The flexibility in their synthesis represents a distinct advantage over other spin systems, enabling the systematic production of samples with desirable properties, for example, with a view to implementing quantum logic gates3,4. Here, we report the observation of quantum interference associated with tunnelling trajectories between states of different total spin length in a dimeric molecular nanomagnet. We argue that the interference is a consequence of the unique characteristics of a molecular Mn12 wheel, which behaves as a molecular dimer with weak ferromagnetic exchange coupling: each half of the molecule acts as a single-molecule magnet, whereas the weak coupling between the two halves gives rise to an extra internal spin degree of freedom within the molecule—that is, its total spin may fluctuate. More importantly, the observation of quantum interference provides clear evidence for quantum-mechanical superpositions involving entangled states shared between both halves of the wheel.