Critical behavior in rectangles with mixed boundaries.

Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical sides of the rectangle have up-spin boundary conditions + and the two horizontal sides with either down-spin boundary conditions - or with free-spin boundary conditions f, exact results are presented for the density profiles of the energy and the order parameter which display a surprisingly rich behavior. The new results follow by means of conformal transformations from known results in the half plane with +-+-+ and +f+f+ boundary conditions. The corners with mixed boundary conditions lead to interesting behavior, even in the limit of a half-infinite strip. The behavior near these corners can be described by a "corner-operator-expansion," which is discussed in the second part of the paper. The analytic predictions agree very well with simulations, with no adjustable parameters.

Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions.

With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane y>0 with different boundary conditions a and b on the negative and positive x axes. For ab=-+ and f+, they determined the one- and two-point averages of the spin σ and energy ε. Here +,-, and f stand for spin-up, spin-down, and free-spin boundaries, respectively. The case +-+-+⋯, where the boundary condition switches between + and - at arbitrary points, ζ_{1},ζ_{2},⋯ on the x axis was also analyzed. In the first half of this paper a similar study is carried out for the alternating boundary condition +f+f+⋯ and the case -f+ of three different boundary conditions. Exact results for the one- and two-point averages of σ,ε, and the stress tensor T are derived with conformal-invariance methods. From the results for 〈T〉, the critical Casimir interaction with the boundary of a wedge-shaped inclusion is derived for mixed boundary conditions. In the second half of the paper, arbitrary two-dimensional critical systems with mixed boundary conditions are analyzed with boundary-operator expansions. Two distinct types of expansions-away from switching points of the boundary condition and at switching points-are considered. Using the expansions, we express the asymptotic behavior of two-point averages near boundaries in terms of one-point averages. We also consider the strip geometry with mixed boundary conditions and derive the distant-wall corrections to one-point averages near one edge due to the other edge. Finally we confirm the consistency of the predictions obtained with conformal-invariance methods and with boundary-operator expansions, in the the first and second halves of the paper.

Density profiles around nanoparticles and distant perturbations.

We investigate how density profiles around a spherical nanoparticle in a critical solvent are affected by distant perturbations such as a wall or other particles. Using a new type of "fusion expansion," we evaluate the isotropic and anisotropic changes in the densities at distances r from the sphere center which are of the order of the sphere radius R, with both R and r much smaller than the correlation length and the distance between the sphere and the perturbations. Our results bridge the gap between the changes in the region 0

Casimir interaction of rodlike particles in a two-dimensional critical system.

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

Critical Casimir torques and forces acting on needles in two spatial dimensions.

We investigate the universal orientation-dependent interactions between nonspherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at bulk criticality. For a needle in an Ising strip, the interaction on mesoscopic scales depends on the width of the strip and the length, position, and orientation of the needle. By lattice Monte Carlo simulations we evaluate the free-energy difference between needle configurations being parallel and perpendicular to the strip. We concentrate on small but nonetheless mesoscopic needle lengths for which analytic predictions are available for comparison. All combinations of boundary conditions for the needles and boundaries are considered which belong to either the "normal" or the "ordinary" surface universality class, i.e., which induce local order or disorder, respectively. We also derive exact results for needles of arbitrary mesoscopic length, in particular for needles embedded in a half plane and oriented perpendicularly to the corresponding boundary as well as for needles embedded at the center line of a symmetric strip with parallel orientation.

Polymer depletion profiles around nonspherical colloidal particles.

We study the effect of chain self-avoidance on the polymer density profiles that are induced by a single colloidal particle of nonspherical shape such as an ellipsoid, a dumbbell, or a lens in a solution of nonadsorbing polymers. For colloid sizes sigma much smaller than the size R(x) of the polymers, we observe a pronounced difference between ideal and self-avoiding chains. In the case of ideal polymers, the surfaces of constant density always have the same character as the surface of the particle, e.g., are oblate for an oblate ellipsoid. In the self-avoiding case, however, the character changes with increasing distance r from the particle, and an oblate particle induces prolate surfaces of constant density if sigma<

Anisotropic colloidal particles interacting with polymers in a good solvent.

We study the consequences of chain self-avoidance for the interaction between nonadsorbing polymers and colloidal particles of anisotropic shape, such as ellipsoids, lenses, and dumbbells. In the framework of a field theoretic operator expansion for small mesoscopic particles, we obtain exact results for self-avoiding polymers in d=2 spatial dimensions and we compare ideal and self-avoiding polymers in 2

Long flexible polymers interacting with ellipsoids, cylinders, and needles.

The depletion interactions of ellipsoidal colloidal particles in a solution of long polymer chains are analyzed. Of primary concern are the limiting cases in which the ellipsoid reduces to a cylinder of infinite length and finite radius and a "needle" of finite length and vanishing radius. Relations are obtained between the polymer effects induced by a needle that is much shorter than the polymer size and by a cylinder with radius much smaller than the polymer size. These imply exact quantitative results for the orientation-dependent depletion interaction between a short needle and a wall. Qualitative differences between the needle and thin disk are discussed.

Anisotropic colloidal particles in critical fluids.

We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluid mixture. The orientation-dependent long-ranged universal interactions mediated by the critical solvent between a particle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to the correlation length and interparticle distances. Exact results are obtained using a "small particle operator expansion." The amplitudes of the isotropic and anisotropic operators in the expansion depend on the size and aspect ratio of the dumbbell or lens and are determined by density profiles in the Ising model at the critical point in a wedge geometry with symmetry-breaking fixed-spin boundary conditions. Dumbbells and ellipsoids with a symmetry preserving surface are also considered.

Polymer depletion effects near mesoscopic particles.

The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres, quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modeling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.

[Special aspects of physical training during the rehabilitation stage of coronary patients]. / Besondere Gesichtspunkte des körperlichen Trainings während der Rehabilitationsphase von Koronarpatienten.

Practical aspects: Physical exercise is a basic component of the rehabilitation program for patients recuperating from myocardial infarction or bypass surgery. The aim of exercise is to enhance physical performance by improving coordination, flexibility, strength, speed and endurance. The training concept is matched to the individual capability, which is determined by an exercise test at the beginning of the rehabilitation program. On the basis of this test, an "exercise heart rate" is calculated with the aim of protecting the patient from overstrenuous activity. Depending on their physical fitness, the patients are divided into two groups: those with a capability of less, and those with a capability of more than 1 watt/kg. Most elderly patients are no longer active participants in sports, so that guidance through flexibility and coordination exercise is offered. Usually, patients perform a daily program of 15 minutes of physical activity in their individual groups, and spend 45 minutes walking and relaxing. In addition, they have opportunities for swimming, jogging and cycling. Decreased left-ventricular function: The effects of a four-week training program in myocardial infarction (MI) patients with moderate-to-severe left-ventricular dysfunction were investigated in two distinct studies. In neither study was a deterioration in the ejection fraction at rest or during exercise observed. In the second study, an additional parameter was provided by the Swan-Ganz catheter. Neither pulmonary wedge pressure (PWP) nor cardiac output indicated any deterioration in response to dosed training. However, in this second study, four patients in the training group with a resting ejection fraction (EF) less than 30% developed complications. All these patients had a pathological PWP at rest. Nevertheless, five patients with an EF less than 30% but with a normal PWP at rest completed the training program without complications. The long-term prognosis for training post-MI patients with severe left-ventricular dysfunction would appear to be no worse than for controls. Results of the first study: During the four-week training program, no complications occurred. No major changes in the EF at rest and during training were seen. In the training group the EF at rest increased slightly to 40 +/- 10%. The EF during exercise improved to 39 +/- 10%. Delta EF showed a decrease of 3 +/- 8%. After the four-week training period the decrease was 1 +/- 9%. In the control group, a major increase in the EF at rest to 41 +/- 10% was seen. The EF during exercise, however, showed only a small increase to 43 +/- 15%.(ABSTRACT TRUNCATED AT 400 WORDS)

[A survey of the medical and psychosocial status of 140 workers 32 months following myocardial infarct]. / Eine Befragung zur medizinischen und psychosozialen Situation von 140 Arbeiterinnen 32 Monate nach Myokarderstinfarkt.

We suspected there could be different social, psychological, and medical problems for women after a first myocardial infarction than those affecting men. 140 women (56.4 +/- 7 years) were interviewed by questionnaire 32 +/- 8.7 months after myocardial infarction; 83% (n = 119) responded (8.8% of the sample group had died), 12% suffered a reinfarction, and 11% underwent aortocoronary bypass surgery. For 84% of those responding it was harder to do their housework after myocardial infarction, but 73% did it without help. 51.5% showed a mood change that included increasing depression, anxiousness, and insecurity. In 12.5% of the women their relationship with their husband was adversely affected; in 6.6% their relationship with their children worsened. 83% (n = 89) saw their infarction as a result of stress. 45% could not relieve their stress after 32 months. A subjective feeling of stress decrease in 54% was achieved with a quieter life, in 39.5% by resigning their jobs, and in 6.5% by the death of the husband. Concerning somatic risk factors 74% of the smokers stopped smoking; oral contraceptives were discontinued in all cases. 90.5% (n = 97) of the women said they had their serum lipid values checked regularly, but these were only under control in 35%. We conclude the rehabilitation process does not end when patients leave a rehabilitation clinic. Patients should acquire household help, and their family situation should be discussed during their stay in the rehabilitation clinic. Concerning the somatic risk factors, women who survive myocardial infarction require better care and information.

[A set of questionnaires for the assessment (screening) of psychological disorders and social problems in cardiac rehabilitation patients]. / Ein Fragebogenset zur Erfassung (Screening) psychischer Störungen und sozialer Probleme von Patienten in der kardiologischen Rehabilitation.

A set of questionnaires for the assessment (screening) of psychological and social problems in cardiac rehabilitation patients is analyzed for its psychometric properties. The test battery had before been consented by a task force of the German Association for the Prevention and Rehabilitation of Cardiovascular Disease, DGPR. It integrates generally approved and well-tried assessments for depression/anxiety, social isolation (vocational) stress, and subjective vocational disability. The questionnaire was administered to a convenience sample of 426 patients undergoing inpatient cardiac rehabilitation. Results on the psychometric properties, a comparison of the cardiac sample to the general population, as well as distributions of quartile ranges are reported. Also, a preliminary appraisal of the need for further assessment or treatment is made. The results confirm that the short test battery is suited for assessing psychological and social problems in cardiac rehabilitation patients.