Shapes for maximal coverage for two-dimensional random sequential adsorption

The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which maximizes the saturated packing fraction. It is found that a concave shape derived from a dimer of disks gives a packing fraction of 0.5833, which is comparable to the maximum packing fraction of ellipsoids and spherocylinders and higher than any other studied shape. Discussion why this shape is so beneficial for random sequential adsorption is given.Comment: 6 pages, 8 figures, 3 table

Unified molecular field theory of nematic, smectic-A, and smectic-C phases

A unified mean-field molecular theory of nematic (NU), smectic A (SmA), and smectic C (SmC) liquid crystal phases, composed of uniaxial nonpolar molecules, is developed taking into account the variation of all orientational and translational order parameters in these phases. Numerical results, obtained by direct global minimization of the free energy, are presented in the form of three typical phase diagrams of different topology. Temperature variation of the relevant order parameters in different sequences of phases is analyzed for various cross sections of the phase diagrams. The present model enables one to reproduce all possible sequences of phase transitions between the given phases including isotropic (Iso)-NU-SmA-SmC, Iso-NU-SmC, Iso-SmA-SmC, and Iso-SmC. The properties of the NAC point, where the NU, SmA, and SmC structures coexist, are considered in detail and the shape of the phase diagram in the vicinity of the NAC point is compared with existing experimental data

Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

It is generally accepted that the transition into the twist–bend nematic phase (NTB) is driven by an elastic instability related to the reduction of the bend elastic constant. Here we use a molecular–statistical theory to show that sufficiently strong polar interactions between bent–shaped molecules may lead to experimentally observed reduction of the bend elastic constant in the nematic phase even if electrostatic dipole-dipole interactions are not taken into account. We propose a simple model of bent–core particles and derive explicit analytical expressions which enable one to understand how polar molecular shape affects the elastic constants, and, in particular, the important role of the bend angle. Numerical graphs showing temperature variations of all elastic constants are also presented including the variation of the bend and splay elastic constants before and after the renormalization determined by local polar order of molecular steric dipoles and the corresponding polar correction to the one–particle distribution function

Stability of Biaxial Nematic Phase for Systems with Variable Molecular Shape Anisotropy

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean field model of Mulder and Ruijgrok [Physica A {\bf 113}, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems - a mixture of potassium laurate, 1-decanol, and $D_2O$, where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimeric- or tetrapod-like molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.Comment: 18 pages containing 6 figure

Trajectories in physical functioning at older age in relation to childhood and adulthood SES and social mobility: a population-based cohort study

INTRODUCTION: Older age is associated with the deterioration of physical functioning (PF), and low PF is strongly related to poor quality of life among older people. We conducted a study to examine the trajectories of PF between middle and old age, considering sex differences as well as the association between socioeconomic status (SES) at different life stages and changes in PF. METHODS: We analyzed data from the Polish arm of the HAPIEE (Health, Alcohol and Psychosocial factors In Eastern Europe) study, including 1,116 men and 1,178 women aged 45–64 years at baseline. Adult and childhood SES and social mobility were assessed using a retrospectively focused questionnaire. PF was assessed using the 10-question SF-36 scale at baseline examination, face-to-face re-examination, and three postal surveys, covering up to 20 years (on average, 18 years). We employed Generalized Estimating Equations models to assess changes in PF scores over time and compare PF trajectories across different SES categories. RESULTS: After adjusting for age and other covariates, we found that, in both sexes, participants with always middle or high SES, as well as those who reported upward mobility, had higher PF scores at baseline compared to those with always low SES. A decline in PF between middle and old age was observed in all SES groups; however, the decline was slower in participants with always middle or high SES compared to those with always low SES. CONCLUSION: This cohort study revealed that lower SES and downward social mobility were cross-sectionally associated with poorer PF, while upward social mobility seemed to largely reverse the effect of low childhood SES. In addition to the cross-sectional associations observed at baseline, advantaged SES was also significantly associated with a slower decline in PF over an 18-year follow-up period

Changes in Socioeconomic Status as Predictors of Cardiovascular Disease Incidence and Mortality: A 10-Year Follow-Up of a Polish-Population-Based HAPIEE Cohort

Although the inverse association between socioeconomic status (SES) and cardiovascular disease (CVD) is well established, research on the effect of changes in the SES throughout life on CVD risk in populations with different social backgrounds remains scarce. This study aimed to assess the relationship between childhood SES, adulthood SES, and changes in SES over time, and CVD incidence and mortality in a Polish urban population. In addition, the predictive performance of the SES index was compared with education alone. A cohort study with a 10-year follow-up was conducted, in which a random sample of 10,728 residents in Kraków aged 45–69 years were examined. The SES was assessed at baseline using data on education, parents’ education, housing standard at the age of 10 years, professional activity, household amenities, and difficulties in paying bills and buying food. SES categories (low, middle, and high) were extracted using cluster analyses. Information on new CVD cases was obtained from questionnaires in subsequent phases of the study and confirmed by reviewing clinical records. Data on deaths and causes were obtained from the residents’ registry, Central Statistical Office, and the participants’ families. The effect of the SES index on the risk of CVD was assessed using Cox proportional hazard models. In male and female participants, the CVD incidence and mortality were observed to be 27,703 and 32,956 person-years (384 and 175 new CVD cases) and 36,219 and 40,048 person-years (159 and 92 CVD deaths), respectively. Childhood SES was not associated with CVD incidence and mortality. A protective effect of high adulthood SES against CVD mortality was observed in men and women (HR = 0.59, 95% CI = 0.31–0.97; HR = 0.33, 95% CI = 0.14–0.75, respectively). In women, downward social mobility was related to 2.24 and 3.75 times higher CVD incidence and mortality, respectively. In men, a protective effect against mortality was observed in upward mobility (HR = 0.50, 95% CI = 0.29–0.84). Model discrimination was similar for the SES index and education alone for the association with CVD incidence. In women, the SES index was a slightly better predictor of CVD mortality than education alone (C-index = 0.759, SE = 0.0282 vs. C-index = 0.783, SE = 0.0272; p = 0.041). In conclusion, high adulthood SES, but not childhood SES, may be considered to be a protective factor against CVD in urban populations in high-CVD-risk regions. No effects of critical periods in early life were observed on CVD risk. In later life, social mobility was found to affect CVD mortality in both men and women. In men, a protective effect of upward mobility was confirmed, whereas in women, an increased CVD risk was related to downward mobility. It can be concluded that CVD prevention may be beneficial if socioeconomic potentials are strengthened in later life

Accumulation of psychosocial risk factors and incidence of cardiovascular disease: a prospective observation of the Polish HAPIEE cohort

BACKGROUND: Psychosocial risk factors for cardiovascular disease (CVD) are known to cluster in individuals, but the effect of cumulative exposure has not been thoroughly described in terms of CVD risk. AIMS: The aim of the study was to assess the relationship between accumulation of psychosocial risk factors such as low education, material deprivation, depressive symptoms, and low perceived control and the risk of incident CVD. METHODS: This cohort study with 11‑year follow‑up included a random population sample (age, 45-69 years). Psychosocial factors were assessed using standard tools. Accumulation of psychosocial risk factors was determined by summing up the number of psychosocial factors experienced. The risk of incident CVD depending on the number of psychosocial factors was estimated (reference, no psychosocial factors). Cox proportional hazards models were fitted. RESULTS: In total, 43 572 and 51 772 person‑years were analyzed. There were 479 and 291 new CVD cases in men and women, respectively. An age‑adjusted model showed an increase in CVD risk in men exposed to 3 and 4 psychosocial risk factors by nearly 60% and 125%, respectively (P <0.05). Further adjustment waved the association in individual strata, but a significant linear trend was observed. In women, in a fully adjusted model, the second and subsequent risk factors increased the risk of CVD by nearly 70% up to over 2‑fold (P <0.001). The total population attributable risk associated with exposure to psychosocial risk factors in women was 34.1%. CONCLUSIONS: The accumulation of psychosocial risk factors was associated with increased risk of CVD. In men, the relation was substantially explained by classic risk factors. In women, about one-third of incident CVD cases could be attributed to psychosocial risk factors

A Mediterranean-type diet is associated with better metabolic profile in urban Polish adults: Results from the HAPIEE study

The aim of this study was to evaluate the relationship between adherence to a Mediterranean-type diet and metabolic syndrome (MetS) in the Polish arm of the Health, Alcohol and Psychosocial factors In Eastern Europe (HAPIEE) cohort study