Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces

The limit n to infinity of the classical O(n) phi^4 model on a 3d film with free surfaces is studied. Its exact solution involves a self-consistent 1d Schr\"odinger equation, which is solved numerically for a partially discretized as well as for a fully discrete lattice model. Numerically exact results are obtained for the scaled Casimir force at all temperatures. Obtained via a single framework, they exhibit all relevant qualitative features of the thermodynamic Casimir force known from wetting experiments on Helium-4 and Monte Carlo simulations, including a pronounced minimum below the bulk critical point.Comment: 5 pages, 2 figure

The role of antibiotics in the treatment of chronic prostatitis: A consensus statement

Practical guidelines for the diagnosis and treatment of chronic prostatitis are presented. Chronic prostatitis is classified as chronic bacterial prostatitis (culture-positive) and chronic inflammatory prostatitis (culture-negative). If chronic bacterial prostatitis is suspected, based on relevant symptoms or recurrent UTIs, underlying urological conditions should be excluded by the following tests: rectal examination, midstream urine culture and residual urine. The diagnosis should be confirmed by the Meares and Stamey technique. Antibiotic therapy is recommended for acute exacerbations of chronic prostatitis, chronic bacterial prostatitis and chronic inflammatory prostatitis, if there is clinical, bacteriological or supporting immunological evidence of prostate infection. Unless a patient presents with fever, antibiotic treatment should not be initiated immediately except in cases of acute prostatitis or acute episodes in a patient with chronic bacterial prostatitis. The work-up, with the appropriate investigations should be done first, within a reasonable time period which, preferably, should not be longer than 1 week. During this period, nonspecific treatment, such as appropriate analgesia to relieve symptoms, should be given. The minimum duration of antibiotic treatment should be 2-4 weeks. If there is no improvement in symptoms, treatment should be stopped and reconsidered. However, if there is improvement, it should be continued for at least a further 2-4 weeks to achieve clinical cure and, hopefully, eradication of the causative pathogen. Antibiotic treatment should not be given for 6-8 weeks without an appraisal of its effectiveness. Currently used antibiotics are reviewed. Of these, the fluoroquinolones ofloxacin and ciprofloxacin are recommended because of their favourable antibacterial spectrum and pharmacokinetic profile. A number of clinical trials are recommended and a standard study design is proposed to help resolve some outstanding issues

Thermodynamic Casimir effects involving interacting field theories with zero modes

Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature $T_{c,\infty}$ (thermodynamic Casimir effect) are investigated below the upper critical dimension $d^*=4$ by means of field-theoretic renormalization group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero modes that are present in Landau theory at $T_{c,\infty}$ make conventional RG-improved perturbation theory in $4-\epsilon$ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures T\geqT_{c,\infty} as functions of $\mathsf{L}\equiv L/\xi_\infty$, where $\xi_\infty$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained whose $\mathsf{L}\to0$ limits are in conformity with previous results for the Casimir amplitudes $\Delta_C$ to $O(\epsilon^{3/2})$ and display a more reasonable small-$\mathsf{L}$ behavior inasmuch as they approach the critical value $\Delta_C$ monotonically as $\mathsf{L}\to 0$.Comment: 23 pages, 10 figure

Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results

We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as $b x^{-(d+\sigma)}$ as $x\to\infty$, with $2<\sigma<4$ and $2<d+\sigma\leq 6$, on the Casimir effect at and near the bulk critical temperature $T_{c,\infty}$, for $2<d<4$. For the scaled reduced Casimir force per unit cross-sectional area, we obtain the form L^{d} {\mathcal F}_C/k_BT \approx \Xi_0(L/\xi_\infty) + g_\omega L^{-\omega}\Xi\omega(L/\xi_\infty) + g_\sigma L^{-\omega_\sigm a} \Xi_\sigma(L \xi_\infty). The contribution $\propto g_\sigma$ decays for $T\neq T_{c,\infty}$ algebraically in $L$ rather than exponentially, and hence becomes dominant in an appropriate regime of temperatures and $L$. We derive exact results for spherical and Gaussian models which confirm these findings. In the case $d+\sigma =6$, which includes that of nonretarded van-der-Waals interactions in $d=3$ dimensions, the power laws of the corrections to scaling $\propto b$ of the spherical model are found to get modified by logarithms. Using general RG ideas, we show that these logarithmic singularities originate from the degeneracy $\omega=\omega_\sigma=4-d$ that occurs for the spherical model when $d+\sigma=6$, in conjunction with the $b$ dependence of $g_\omega$.Comment: 28 RevTeX pages, 12 eps figures, submitted to PR

Casimir force in O(n) lattice models with a diffuse interface

On the example of the spherical model we study, as a function of the temperature $T$, the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry $\infty^{d-1}\times L$, where $2<d<4$ is the dimensionality of the system. We consider a system with nearest-neighbor anisotropic interaction constants $J_\parallel$ parallel to the film and $J_\perp$ across it. The model represents the $n\to\infty$ limit of O(n) models with antiperiodic boundary conditions applied across the finite dimension $L$ of the film. We observe that the Casimir amplitude $\Delta_{\rm Casimir}(d|J_\perp,J_\parallel)$ of the anisotropic $d$-dimensional system is related to that one of the isotropic system $\Delta_{\rm Casimir}(d)$ via $\Delta_{\rm Casimir}(d|J_\perp,J_\parallel)=(J_\perp/J_\parallel)^{(d-1)/2} \Delta_{\rm Casimir}(d)$. For $d=3$ we find the exact Casimir amplitude $\Delta_{\rm Casimir}= [ {\rm Cl}_2 (\pi/3)/3-\zeta (3)/(6 \pi)](J_\perp/J_\parallel)$, as well as the exact scaling functions of the Casimir force and of the helicity modulus $\Upsilon(T,L)$. We obtain that $\beta_c\Upsilon(T_c,L)=(2/\pi^{2}) [{\rm Cl}_2(\pi/3)/3+7\zeta(3)/(30\pi)] (J_\perp/J_\parallel)L^{-1}$, where $T_c$ is the critical temperature of the bulk system. We find that the effect of the helicity is thus strong that the Casimir force is repulsive in the whole temperature region.Comment: 15 pages, 3 figure

The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation

The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas

Finite-size effects in the spherical model of finite thickness

A detailed analysis of the finite-size effects on the bulk critical behaviour of the $d$-dimensional mean spherical model confined to a film geometry with finite thickness $L$ is reported. Along the finite direction different kinds of boundary conditions are applied: periodic $(p)$, antiperiodic $(a)$ and free surfaces with Dirichlet $(D)$, Neumann $(N)$ and a combination of Neumann and Dirichlet $(ND)$ on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary $d$. It is found, for $2<d<4$, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for $(p)$ and $(a)$. For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At $d=3$, the critical amplitude of the singular part of the free energy (related to the so called Casimir amplitude) is estimated. We obtain $\Delta^{(p)}=-2\zeta(3)/(5\pi)=-0.153051...$, $\Delta^{(a)}=0.274543...$ and $\Delta^{(ND)}=0.01922...$, implying a fluctuation--induced attraction between the surfaces for $(p)$ and repulsion in the other two cases. For $(D)$ and $(N)$ we find a logarithmic dependence on $L$.Comment: Version published in J. Phys. A: Math. Theo

The translation, validity and reliability of the German version of the Fremantle Back Awareness Questionnaire

Background: The Fremantle Back Awareness Questionnaire (FreBAQ) claims to assess disrupted self-perception of the back. The aim of this study was to develop a German version of the Fre-BAQ (FreBAQ-G) and assess its test-retest reliability, its known-groups validity and its convergent validity with another purported measure of back perception. Methods: The FreBaQ-G was translated following international guidelines for the transcultural adaptation of questionnaires. Thirty-five patients with non-specific CLBP and 48 healthy participants were recruited. Assessor one administered the FreBAQ-G to each patient with CLBP on two separate days to quantify intra-observer reliability. Assessor two administered the FreBaQ-G to each patient on day 1. The scores were compared to those obtained by assessor one on day 1 to assess inter-observer reliability. Known-groups validity was quantified by comparing the FreBAQ-G score between patients and healthy controls. To assess convergent validity, patient\u27s FreBAQ-G scores were correlated to their two-point discrimination (TPD) scores. Results: Intra- and Inter-observer reliability were both moderate with ICC3.1 = 0.88 (95%CI: 0.77 to 0.94) and 0.89 (95%CI: 0.79 to 0.94), respectively. Intra- and inter-observer limits of agreement (LoA) were 6.2 (95%CI: 5.0±8.1) and 6.0 (4.8±7.8), respectively. The adjusted mean difference between patients and controls was 5.4 (95%CI: 3.0 to 7.8, p\u3c0.01). Patient\u27s FreBAQ-G scores were not associated with TPD thresholds (Pearson\u27s r = -0.05, p = 0.79). Conclusions: The FreBAQ-G demonstrated a degree of reliability and known-groups validity. Interpretation of patient level data should be performed with caution because the LoA were substantial. It did not demonstrate convergent validity against TPD. Floor effects of some items of the FreBAQ-G may have influenced the validity and reliability results. The clinimetric properties of the FreBAQ-G require further investigation as a simple measure of disrupted self-perception of the back before firm recommendations on its use can be made