The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.Comment: 19 pages, 9 figures; v2: references added, some changes in the tex

Oronasopharyngeal chordomas

ManuscriptBackground: Chordomas are rare tumors derived from notochordal remnants. The authors report on a series of three cases of primary familial oronasopharyngeal chordomas treated at our institution. Methods: A retrospective chart review was completed of the three cases of primary familial oronasopharyngeal chordoma treated at the University of Utah. Findings: All three patients (100%) were neurologically intact and presented with nasal obstruction. The patients ranged in age from 5 to 65 years and were first-degree relatives. None of the patients had bony erosion of the skull base on imaging, and all of the patients' tumors connected with the skull base via a tract. All three patients were treated with a wide excision combined with drilling of the involved skull base. They all tolerated the procedure without any complications and remain tumor free with a follow up of 12 months to 4.5 years. Conclusion: Primary oronasopharyngeal chordomas are rare tumors that may present without bony erosion of the skull base. A wide excision with drilling of the involved bony structures may offer an oncologic cure

Transition from Knudsen to molecular diffusion in activity of absorbing irregular interfaces

We investigate through molecular dynamics the transition from Knudsen to molecular diffusion transport towards 2d absorbing interfaces with irregular geometry. Our results indicate that the length of the active zone decreases continuously with density from the Knudsen to the molecular diffusion regime. In the limit where molecular diffusion dominates, we find that this length approaches a constant value of the order of the system size, in agreement with theoretical predictions for Laplacian transport in irregular geometries. Finally, we show that all these features can be qualitatively described in terms of a simple random-walk model of the diffusion process.Comment: 4 pages, 4 figure

Surface barriers as dominant mechanism to transport limitations in hierarchically structured catalysts – Application to the zeolite-catalyzed alkylation of benzene with ethylene

The meso-macropore network of a hierarchically structured zeolite catalyst is numerically optimized to maximize the volume-integrated reaction yield in the ethylation of benzene to produce ethylbenzene over zeolite H-ZSM-5. A hierarchical approach is used at multiple length scales to determine the optimal pore network properties. The maximum volume-integrated reaction yield of the hierarchically structured zeolite catalyst containing meso- and macropores is nearly twice the yield of a zeolite pellet containing only macropores, at the same macroporosity. To bridge the gap between modeling and experiments, a series of physical mixtures of ZSM-5 crystals and mesoporous silica, containing different weight fractions of zeolite is synthesized and used in fixed bed reactor experiments to determine the optimal pellet structure to maximize the conversion of ethylene. Comparison with reactor simulations of the zeolite composites shows that the performance of the zeolite composites might be limited by surface barriers at the external surface of the zeolite crystals, rather than by diffusion limitations within the meso-macropore network of the pellets

Billiards in a general domain with random reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord "picked at random" in ${\mathcal D}$, and we study the angle of intersection of the process with a $(d-1)$-dimensional manifold contained in ${\mathcal D}$.Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains

Steady-State Properties of Single-File Systems with Conversion

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption and reaction rate constants on the steady-state properties of Single-File Systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions and Monte-Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between Mean-Field and the simulations are found when rates of diffusion are high. Mean-Field results only include Single-File behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.Comment: 15 pages, 20 figure

Transient behavior in Single-File Systems

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption and reaction rates on the transient properties of Single-File Systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions, Cluster Approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where Mean-Field analysis gives good results compared to Dynamic Monte-Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distribution of the sites both for Mean-Field and simulations are compared. Different results for slow and fast reaction systems and different distribution of reactive sites are discussed.Comment: 18 pages, 19 figure

Age-related differences in the control of weight-shifting within the surface of support

BACKGROUND AND AIM: An important reason for falling in elderly is incorrect weight-shifting¹. In many daily life activities quick and accurate weight-shifting is needed to maintain balance, especially in situations when balance is suddenly disturbed and anticipation on the upcoming movement is difficult. Considering the deterioration in postural control in elderly², it is expected that they have more difficulties with executing these quick and accurate weight-transfers³. The present study aims to gain more insight in age-related differences in postural control strategies during a postural control task requiring weight-transfers of different amplitudes and in different directions within the surface of support METHODS: Nine healthy older adults (70.3±6.9 years) and twelve young adults (20.9±0.5 years) participated in the study. The participants performed a weight-shifting task by moving the whole body in different directions to move a cursor, representing real time COP position, towards targets of different sizes and at different distances projected on a screen. Movement time (MT) was the time between the appearance of the goal target and the moment a target switch was realized (i.e. the cursor stayed in the goal target for 0.5 second). The accuracy of the movement was quantified by Counts on Goal (CoG), that is the number of times the cursor hit the goal target before a target switch was realized and by Dwelling Time (DT), the time required to realize a target switch after the goal target was hit by the cursor for the first time. Fluency was expressed by the maximal deviation (MD) of the performed path with respect to the ideal path and the number of peaks (nP), or inflections in the performed path. RESULTS: Significant main effects of target size, target distance and age on all outcome measures were found (p<.01). With decreasing target size, increasing target distance and increasing age, MT significantly increased and fluency and accuracy significantly decreased (nP, MD, CoG and DT increased). Elderly used a slower, less accurate and less fluent weight-shifting strategy compared to younger adults with increasing task difficulty (e.g. decreasing target size and increasing target distance) as indicated by significant interaction effects of size*age and distance*age (p<.05). CONCLUSION: The results of this study provided insight in how elderly control their weight-shifting when the movement cannot be anticipatorily planned. Elderly exhibited slower and more variable movements, especially with increasing task difficulty. This weight-shifting strategy seems characterizing for an increased fall risk in elderly, since the results indicate that elderly might have more difficulties with executing an adequate (quick and accurate) adaptation to a perturbation in daily life. ¹SN Robinovitch et al. Lancet. (2013), 381(9860), 47-54. ²FB Horak. Age Ageing. (2006), 35(2), 7-11. ³V Jongman et al. Stud Health Technol Inform. (2012), 181, 93-97

Oxygen Moment Formation and Canting in Li2CuO2

The possibilities of oxygen moment formation and canting in the quasi-1D cuprate Li2CuO2 are investigated using single crystal neutron diffraction at 2 K. The observed magnetic intensities could not be explained without the inclusion of a large ordered oxygen moment of 0.11(1) Bohr magnetons. Least-squares refinement of the magnetic structure of Li2CuO2 in combination with a spin-density Patterson analysis shows that the magnetization densities of the Cu and O atoms are highly aspherical, forming quasi-1D ribbons of localised Cu and O moments. Magnetic structure refinements and low-field magnetization measurements both suggest that the magnetic structure of Li2CuO2 at 2 K may be canted. A possible model for the canted configuration is proposed.Comment: 10 pages, 8 figures (screen resolution

Nonuniform compensation of current density distribution in polymer electrolyte fuel cells by local heating

A homogeneous current density distribution improves a fuel cell’s performance and prolongs its service life. Effective cell structure designs and uniform compression during assembly could support this goal by ensuring a homogeneous reaction rate across the activation area. Due to the coupling of hydro-electro-thermal relationships, for instance, the concentration of reactants along the flow field decreases continuously as the electrochemical reaction proceeds, and the subsequent accumulation of liquid water leads to a low current density at the outlet. The effect of operating conditions, such as local heating, on the current density distribution requires further investigation. This paper studies the impact of local heating on polymer electrolyte fuel cell (PEFC) performance and analyses the effects on voltage by mapping the current density distribution across the active area. Local heating was supplied to the three regions of the electrode, namely, fuel inlet, central and outlet regions, with the latter exhibiting the best performance (in the activation, Ohmic and mass transport controlled region, the output voltage increases compared to no local heating corresponding to 1.28%, 2.17% and 2.46%, respectively). Here, we show that in all local heating cases, outlet heating can compensate for the lowest current density region with the largest current density increased by 91.10 mA cm−2 and achieves a more homogeneous current distribution, while inlet heating aggravates heterogeneity. This study provides practical guidance for optimal thermal management system development whereby the cooling channel design should be locally optimised for more uniform distributions of current density and temperature compared to heating the cell uniformly