Healing Length Research Articles

Cannulated screws plus separate vertical wirings for fixation of acute patella inferior pole fracture

Objective To investigate the feasibility and clinical effect of cannulated screws plus separate vertical wirings technique for acute fracture of the inferior pole of the patella. Methods From May 2012 to September 2013, 14 patients with fresh closed unilateral fracture of the inferior pole of the patella were treated with the cannulated screws plus separate vertical wirings. Eight patients were injured in traffic collisions and 6 in fall accidents. Fracture AO classification was type 34A1 in 8 patients and type 34A2 in 6 patients. Time from injury to operation was 1-7 days (mean, 2.5 days). Number of tie wires was determined according to the degree of fracture comminution. Fracture healing, fixed position and patellar length were evaluated by radiographic examination postoperatively. Knee mobility and Bostman evaluation system were investigated to analyze the clinical effect. Results All the patients obtained average 15-month follow-up (range, 12 to 29 months). At postoperative 2 months, the fracture healed with good alignment of the broken bone and proper place of the internal fixation device noted on the X-ray films. At postoperative 6 and 12 months, X-ray films revealed fracture bony healing, good location of the wire internal fixation, and no apparent shortening of the patella. At the 12 months, range of knee motion was (126.0±4.5) ° for flexion and (2.0±1.7) ° for extension. Bostman functional score for patella fracture was (28.1±1.9)points. And 12 patients were rated as excellent and 2 good, with excellence rate of 100%. Conclusion Cannulated screw fixation plus separate vertical wiring is effective to stabilize patella inferior pole fracture and has good results, indicating a recommended surgical method. Key words: Patella; fracture fixation, internal; Cannulated screws

Analysis of experimental data for two-band superconductors at T ≈ Tc using the GL theory in the presence of a self-consistent vortex line

We study the two-component Ginzburg–Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB 2, V 3 Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V 3 Si and LiFeAs , while is T-dependent for the compound MgB 2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V 3 Si and LiFeAs seems to be different from the one in MgB 2. The use of this parameter, κ, as a new way to "study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism.

Rydberg Electrons in a Bose-Einstein Condensate

We investigate a hybrid system composed of ultracold Rydberg atoms immersed in an atomic Bose-Einstein condensate (BEC). The coupling between Rydberg electrons and BEC atoms leads to excitations of phonons, the exchange of which induces a Yukawa interaction between Rydberg atoms. Because of the small electron mass, the effective charge associated with this quasiparticle-mediated interaction can be large. Its range, equal to the BEC healing length, is tunable using Feshbach resonances to adjust the scattering length between BEC atoms. We find that for small healing lengths, the distortion of the BEC can "image" the Rydberg electron wave function, while for large healing lengths the induced attractive Yukawa potentials between Rydberg atoms are strong enough to bind them.

Critical velocity for vortex shedding in a Bose-Einstein condensate

We present measurements of the critical velocity for vortex shedding in a highly oblate Bose-Einstein condensate with a moving repulsive Gaussian laser beam. As a function of the barrier height $V_0$, the critical velocity $v_c$ shows a dip structure having a minimum at $V_0 \approx \mu $, where $\mu$ is the chemical potential of the condensate. At fixed $V_0\approx 7\mu$, we observe that the ratio of $v_c$ to the speed of sound $c_s$ monotonically increases for decreasing $\sigma/\xi$, where $\sigma$ is the beam width and $\xi$ is the condensate healing length. The measured upper bound for $v_c/c_s$ is about 0.4, which is in good agreement with theoretical predictions for a two-dimensional superflow past a circular cylinder. We explain our results with the density reduction effect of the soft boundary of the Gaussian obstacle, based on the local Landau criterion for superfluidity.

Finite temperature effective field theory and two-band superfluidity in Fermi gases

We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg-Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov-de Gennes method. The advantage of an effective field theory over Bogoliubov-de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.

Continuous and discontinuous dark solitons in polariton condensates

Bose-Einstein condensates of exciton-polaritons are described by a Schr\"odinger system of two equations. Nonlinearity due to exciton interactions gives rise to a frequency band of dark soliton solutions, which are found analytically for the lossless zero-velocity case. The soliton's far-field value varies from zero to infinity as the operating frequency varies across the band. For positive detuning (photon frequency higher than exciton frequency), the exciton wavefunction becomes discontinuous when the operating frequency exceeds the exciton frequency. This phenomenon lies outside the parameter regime of validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we give a derivation of a single-mode GP model from the initial Schr\"odinger system and compare the continuous polariton solitons and GP solitons using the healing length notion.

Static interfacial properties of Bose-Einstein-condensate mixtures

The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\ensuremath{\xi}}_{1}$ and ${\ensuremath{\xi}}_{2}$ and by the interspecies repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=1/2$ and $K=3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\ensuremath{\xi}}_{1},\phantom{\rule{0.28em}{0ex}}{\ensuremath{\xi}}_{2}$, and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

In-plane gradient-magnetic-field-induced vortex lattices in spin-orbit-coupled Bose-Einstein condensations

We consider the ground-state properties of the two-component spin-orbit coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the non-interacting case, the ground state supports giant-vortices carrying large angular momenta without rotating the trap. The vorticity is highly tunable by varying the amplitudes and orientations of the magnetic field. Interactions drive the system from a giant-vortex state to various configurations of vortex lattice states along a ring. Vortices exhibit ellipse-shaped envelops with the major and minor axes determined by the spin-orbit coupling and healing lengths, respectively. Phase diagrams of vortex lattice configurations are constructed and their stabilities are analyzed.

Edge binding of sine-Gordon solitons in spin-orbit-coupled Bose-Einstein condensates

In recent experiments with ultracold gases a Raman coupling scheme is used to produce both spin-orbit (SO) and Zeeman-type couplings [Y.-J. Lin et al., Nature 471, 83 (2011)]. Their competition drives a phase transition to a magnetized state with broken $Z_2$ symmetry. Using a hydrodynamic approach we study a confined binary condensate subject to both SO and Zeeman-type couplings. We find that in the limit of small healing length and in the phase with unbroken symmetry, the boundary magnetization profile has an analytical solution in the form of a sine-Gordon soliton. The soliton is bound to the edge of the system by the nontrivial boundary condition resulting from the combined effect of the SO coupling and the drop in the particle density. The same boundary condition is important in the magnetized phase as well, where we characterize numerically the boundary spin structure. We further discuss how the nontrivial magnetization structure affects the density profile near the boundary, yet another prediction that can be tested in current experiments of spin-orbit coupled condensates.

Critical wetting, first-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries.

On the momentum of solitons and vortex rings in a superfluid

This paper is devoted to the calculation of the momentum of localized excitations, such as solitons and vortex rings, moving in a superfluid. The direct calculation of the momentum by integration of the mass flux density results in a badly-converging integral. I suggest a method for the renormalization of the integral with the explicit separation of a term related to the vortex line. This term can be calculated explicitly and gives the main contribution for the rings whose size is large compared to the healing length. I compare my method with the Jones and Roberts prescription for renormalization. I investigate the case of a uniform superfluid, and that of a superfluid in a cylindrical trap. I discuss the calculation of the jump in the phase of the order parameter and obtain a simple estimate for this jump.

Surgical infection and malnutrition.

Malnutrition in surgical patients is associated with delayed recovery, higher rates of morbidity and mortality, prolonged hospital stay, increased healthcare costs and a higher early re-admission rate. Data synthesis after review of pertinent literature. The aetiology of malnutrition is multifactorial. In cancer patients, there is an abnormal peripheral glucose disposal, gluconeogenesis, and whole-body glucose turnover. Malnourished cancer patients undergoing major operations are at significant risk from perioperative complications such as infectious complications. Surgical aggression generates an inflammatory response which worsens intermediary metabolism. Nutritional evaluation and nutritional support must be performed in all surgical patients, in order to minimize infectious complications. Enteral nutrition early in the postoperative period is effective and well tolerated reducing infectious complications, improving wound healing and reducing length of hospital stay. Pharmaconutrition is indicated in those patients, who benefit from enteral administration of arginine, omega 3 and RNA, as well as parenteral glutamine supplementation. When proximal sutures are used, tubes allowing early jejunal feeding should be used.

Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

We calculate the pair correlation function and the order parameter correlation function, which probe, respectively, the intrapair and interpair correlations of a Fermi gas with attractive interparticle interaction, in terms of a diagrammatic approach as a function of coupling throughout the BCS-Bose-Einstein condensation (BEC) crossover and of temperature, both in the superfluid and normal phase across the critical temperature ${T}_{c}$. Several physical quantities are obtained from this calculation, including the pair coherence and healing lengths, the Tan's contact, the crossover temperature ${T}^{*}$ below which interpair correlations begin to build up in the normal phase, and the signature for the disappearance of the underlying Fermi surface which tends to survive in spite of pairing correlations. A connection is also made with recent experimental data on the temperature dependence of the normal coherence length as extracted from the proximity effect measured in high-temperature (cuprate) superconductors.

The internal structure of a vortex in a two-dimensional superfluid with long healing length and its implications

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov’s hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov’s action, which, in particular, allows for weak solutions of the Gross–Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.

Extension of the Ginzburg–Landau approach for ultracold Fermi gases below a critical temperature

In the context of superfluid Fermi gases, the Ginzburg–Landau (GL) formalism for the macroscopic wave function has been successfully extended to the whole temperature range where the superfluid state exists. After reviewing the formalism, we first investigate the temperature-dependent correction to the standard GL expansion (which is valid close to Tc). Deviations from the standard GL formalism are particularly important for the kinetic energy contribution to the GL energy functional, which in turn influences the healing length of the macroscopic wave function. We apply the formalism to variationally describe vortices in a strong-coupling Fermi gas in the BEC–BCS crossover regime, in a two-band system. The healing lengths, derived as variational parameters in the vortex wave function, are shown to exhibit hidden criticality well below Tc.

Non-local interactions in a BEC: an analogue gravity perspective

We add a minimal correction term to the local Gross–Pitaevskii equation to represent non-locality in the interactions. We show that the effective minimal non-locality can make the healing length decrease more rapidly with the increase of s-wave scattering length leaving the expression of the velocity of sound unaltered. We discuss the implication of this result for a Bose–Einstein condensate being used as an analogue gravity system. The presented result is important in the context of condensed matter physics as well because one can considerably change the size of a quantized vortex at finite s-wave scattering length by tuning the healing length.

Calcanectomy: Avoiding major amputation in the presence of calcaneal osteomyelitis—A case series

BackgroundCalcaneal osteomyelitis is a surgical diagnosis that may be treated by local, resection or major amputation. ObjectiveTo determine the effectiveness of calcanectomy for treating calcaneal osteomyelitis. MethodWe conducted a retrospective review of patients receiving calcanectomy between 1st April 2005 and 1st October 2011 for calcaneal osteomyelitis. We reviewed these cases to determine healing, rate, microbiological analysis, length of stay, limb salvage rate and survival rate. ResultsThere were 10 patients included in this review. There were 7 with diabetes and 3 without.Mean age of group with diabetes was 64 years, of this group 5/7 healed at a mean of 64 days. Mean length of stay for this group was 49.3±39.4 days. 2 patients required a transtibial amputation. Mean age of group without diabetes was 77 years, healing at a mean of 19 days. Mean length of stay for this group was 14±16.8 days and all survived over 3 years. Microbiological analysis of suspected osteomyelitic bone typically isolated >4 organisms. ConclusionsCalcanectomy is a useful procedure for limb salvage. It may reduce morbidity rates for people with calcaneal osteomyelitis, those with diabetes can expect prolonged wound healing and longer length of stay.

Planck scale physics and Bogoliubov spaces in a Bose-Einstein condensate

We analyze the consequences caused by a deformed dispersion relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the pressure, the speed of sound, and the corresponding healing length. Indeed, we prove that the corrections in the relevant thermodynamic properties associated with the ground state, define a non-trivial function of the density of particles and the deformation parameters, allowing us to constrain, in principle, the form of the modified energy-momentum dispersion relation.

Analytical model for self-heating in nanowire geometries

An analytical closed form diffusive model is developed of Joule heating in a device consisting of a nanowire connected to two contacts on a substrate. This analytical model is compared to finite-element simulations and demonstrates excellent agreement over a wider range of system parameters in comparison to other recent models, with particularly large improvements in cases when the width of the nanowire is less than the thermal healing length of the contacts and when the thermal resistance of the contact is appreciable relative to the thermal resistance of the nanowire. The success of this model is due to more accurately accounting for the heat spreading within the contact region of a device and below the nanowire into a substrate. The heat spreading is achieved by matching the linear heat flow near the nanowire interfaces with a radially symmetric spreading solution through an interpolation function. Additional features of this model are the ability to incorporate contact resistances that may be present at the nanowire-contact interfaces, as well as accommodating materials with a linear temperature-dependent electrical resistivity.

Hawking radiation correlations in Bose-Einstein condensates using quantum field theory in curved space

The density-density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used, provided the profile of the flow varies smoothly on scales compared to the condensate healing length.