Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication with a reference added and minor corrections. Phys. Rev. B, in pres

Functional and quality of life outcomes of localised prostate cancer treatments (prostate testing for cancer and treatment [ProtecT] study)

Objective To investigate the functional and quality of life (QoL) outcomes of treatments for localised prostate cancer and inform treatment decision-making. Patients and Methods Men aged 50–69 years diagnosed with localised prostate cancer by prostate-specific antigen testing and biopsies at nine UK centres in the Prostate Testing for Cancer and Treatment (ProtecT) trial were randomised to, or chose one of, three treatments. Of 2565 participants, 1135 men received active monitoring (AM), 750 a radical prostatectomy (RP), 603 external-beam radiotherapy (EBRT) with concurrent androgen-deprivation therapy (ADT) and 77 low-dose-rate brachytherapy (BT, not a randomised treatment). Patient-reported outcome measures (PROMs) completed annually for 6 years were analysed by initial treatment and censored for subsequent treatments. Mixed effects models were adjusted for baseline characteristics using propensity scores. Results Treatment-received analyses revealed different impacts of treatments over 6 years. Men remaining on AM experienced gradual declines in sexual and urinary function with age (e.g., increases in erectile dysfunction from 35% of men at baseline to 53% at 6 years and nocturia similarly from 20% to 38%). Radical treatment impacts were immediate and continued over 6 years. After RP, 95% of men reported erectile dysfunction persisting for 85% at 6 years, and after EBRT this was reported by 69% and 74%, respectively (P < 0.001 compared with AM). After RP, 36% of men reported urinary leakage requiring at least 1 pad/day, persisting for 20% at 6 years, compared with no change in men receiving EBRT or AM (P < 0.001). Worse bowel function and bother (e.g., bloody stools 6% at 6 years and faecal incontinence 10%) was experienced by men after EBRT than after RP or AM (P < 0.001) with lesser effects after BT. No treatment affected mental or physical QoL. Conclusion Treatment decision-making for localised prostate cancer can be informed by these 6-year functional and QoL outcomes

Mental models of the day/night cycle

This article presents the results of an experiment which investigated elementary school children&apos;s explanations of the day/night cycle. First, third, and fifth grade children were asked to explain certain phenomena, such as the disappearance of the sun during the night, the disappearance of stars during the day, the apparent movement of the moon, and the alteration of day and night. The results showed that the majority of the children in our sample used in a consistent fashion a small number of relatively well-defined mental models of the earth, the sun, and the moon to explain the day/night cycle. These mental models of the day/night cycle were empirically accurate, logically consistent and revealed some sensitivity on the part of the children to issues of simplicity of explanation. The younger children formed Initial mental models which provided explanations of the day/night cycle based on everyday experience (e.g., the sun goes down behind mountains, clouds cover up the sun). The older children constructed synthetic mental models (e.g., the sun and the moon revolve around the stationary earth every 24 hours; the earth rotates in an up/down direction and the sun and moon are fixed on opposite sides) which represented attempts to synthesize the culturally accepted view with aspects of their Initial models. A few of the older children appeared to have constructed a mental model of the day/night cycle similar to the scientific one. A theoretical framework is outlined which explains the formation of initial, synthetic, and scientific models of the day/night cycle in terms of the reinterpretation of a hierarchy of constraints, some of which are present early in the child&apos;s life, and others which emerge later out of the structure of the acquired knowledge. © 1994

Meltwater pulse recorded in Last Interglacial mollusk shells from Bermuda

The warm climate of Bermuda today is modulated by the nearby presence of the Gulf Stream current. However, iceberg scours in the Florida Strait and the presence of ice-rafted debris in Bermuda Rise sediments indicate that, during the last deglaciation, icebergs discharged from the Laurentide Ice Sheet traveled as far south as subtropical latitudes. We present evidence that an event of similar magnitude affected the subtropics during the Last Interglacial, potentially due to melting of the Greenland Ice Sheet. Using the clumped isotope paleothermometer, we found temperatures ~10°C colder and seawater δ18O values ~2‰ lower than modern in Last Interglacial Cittarium pica shells from Grape Bay, Bermuda. In contrast, Last Interglacial shells from Rocky Bay, Bermuda, record temperatures only slightly colder and seawater δ18O values similar to modern, likely representing more typical Last Interglacial conditions in Bermuda outside of a meltwater event. The significantly colder ocean temperatures observed in Grape Bay samples illustrate the extreme sensitivity of Bermudian climate to broad-scale ocean circulation changes. They indicate routine meltwater transport in the North Atlantic to near-equatorial latitudes, which would likely have resulted in disruption of the Atlantic Meridional Overturning Circulation. These data demonstrate that future melting of the Greenland Ice Sheet, a potential source of the Last Interglacial meltwater event, could have dramatic climate effects outside of the high latitudes