Darboux class of cosmological fluids with time-dependent adiabatic indices

A one-parameter family of time dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. These fluids can be the real cosmological fluids that are encountered at cosmological scales and they could be used as a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. In addition, new types of cosmological scale factors, corresponding to these fluids, are presentedComment: document with the following three latex files: 1) quhm.tex: 17 pages, 10 figs, 16 numbered refs, Honorable Mention GRF 2000, 2) errad.tex: Errata and Addenda (EaA) of 5 pages with 2 figs enclosed, 3) analogy.tex: Negative friction of Darboux cosmological fluids of 4 page

One-parameter Darboux-transformed quantum actions in Thermodynamics

We use nonrelativistic supersymmetry, mainly Darboux transformations of the general (one-parameter) type, for the quantum oscillator thermodynamic actions. Interesting Darboux generalizations of the fundamental Planck and pure vacuum cases are discussed in some detail with relevant plots. It is shown that the one-parameter Darboux-transformed Thermodynamics refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048 regarding a single mode oscillator Carnot cycle are extended in the same Darboux perspective. We also conjecture a Darboux generalization of the fluctuation-dissipation theoremComment: 14 pages, 13 figures, correction of the formula in the text after Eq. 7, accepted at Physica Script

Supersymmetric Fokker-Planck strict isospectrality

I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent (modulational) damping of the spatial part of the nonstationary Fokker-Planck solutions, which I call strictly isospectral damping. At the same time, using an additive decomposition of the nonstationary solutions suggested by the strictly isospectral procedure and by an argument of Englefield [J. Stat. Phys. 52, 369 (1988)], they can be normalized and thus turned into physical solutions, i.e., Fokker-Planck probability densities. There might be applications to many physical processes during their transient periodComment: revised version, scheduled for PRE 56 (1 August 1997) as a B

Signatures of the Unruh effect from electrons accelerated by ultra-strong laser fields

We calculate the radiation resulting from the Unruh effect for strongly accelerated electrons and show that the photons are created in pairs whose polarizations are maximally entangled. Apart from the photon statistics, this quantum radiation can further be discriminated from the classical (Larmor) radiation via the different spectral and angular distributions. The signatures of the Unruh effect become significant if the external electromagnetic field accelerating the electrons is not too far below the Schwinger limit and might be observable with future facilities. Finally, the corrections due to the birefringent nature of the QED vacuum at such ultra-high fields are discussed. PACS: 04.62.+v, 12.20.Fv, 41.60.-m, 42.25.Lc.Comment: 4 pages, 1 figur

Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations

We present an approach to the bright soliton solution of the NLS equation from the standpoint of introducing a constant potential term in the equation. We discuss a `nongauge' bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sech^p solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2Comment: ~4 pages, 3 figures, 16 references, published versio

On arithmetic detection of grey pulses with application to Hawking radiation

Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the `surface' temperature distribution of a small black hole from the spectral measurement of its (Hawking) grey pulse. This problem has been previously considered by Rosu, who used Chen's modified Moebius inverse transform. Here, we hint on a Ramanujan generalization of Chen's modified Moebius inverse transform that may be considered as a special wavelet processing of the remote-sensed grey signal coming from a black hole or any other distant grey sourceComment: 5 pages, published versio

Effect of variations in atelectasis on tumor displacement during radiation therapy for locally advanced lung cancer

Purpose Atelectasis (AT), or collapsed lung, is frequently associated with central lung tumors. We investigated the variation of atelectasis volumes during radiation therapy and analyzed the effect of AT volume changes on the reproducibility of the primary tumor (PT) position. Methods and materials Twelve patients with lung cancer who had AT and 10 patients without AT underwent repeated 4-dimensional fan beam computed tomography (CT) scans during radiation therapy per protocols that were approved by the institutional review board. Interfraction volume changes of AT and PT were correlated with PT displacements relative to bony anatomy using both a bounding box (BB) method and change in center of mass (COM). Linear regression modeling was used to determine whether PT and AT volume changes were independently associated with PT displacement. PT displacement was compared between patients with and without AT. Results The mean initial AT volume on the planning CT was 189 cm3 (37-513 cm3), and the mean PT volume was 93 cm3 (12-176 cm3). During radiation therapy, AT and PT volumes decreased on average 136.7 cm3 (20-369 cm3) for AT and 40 cm3 (−7 to 131 cm3) for PT. Eighty-three percent of patients with AT had at least one unidirectional PT shift that was greater than 0.5 cm outside of the initial BB during treatment. In patients with AT, the maximum PT COM shift was ≥0.5 cm in all patients and \u3e1 cm in 58% of patients (0.5-2.4 cm). Changes in PT and AT volumes were independently associated with PT displacement (P \u3c .01), and the correlation was smaller with COM (R2 = 0.58) compared with the BB method (R2 = 0.80). The median root mean squared PT displacement with the BB method was significantly less for patients without AT (0.45 cm) compared with those with AT (0.8cm, P = .002). Conclusions Changes in AT and PT volumes during radiation treatment were significantly associated with PT displacements that often exceeded standard setup margins. Repeated 3-dimensional imaging is recommended in patients with AT to evaluate for PT displacements during treatment. Summary This study analyzed 12 patients with atelectasis and 10 patients without atelectasis who underwent repeat 4-dimensional fan beam computed tomography during radiation therapy. Patients with atelectasis had significantly greater tumor displacements than patients without atelectasis, and these tumor displacements often exceeded standard setup margins. Patients with atelectasis may benefit from repeated 3-dimensional imaging during radiation therapy and possible replanning for large tumor displacements

Effect of variations in atelectasis on tumor displacement during radiation therapy for locally advanced lung cancer

Purpose Atelectasis (AT), or collapsed lung, is frequently associated with central lung tumors. We investigated the variation of atelectasis volumes during radiation therapy and analyzed the effect of AT volume changes on the reproducibility of the primary tumor (PT) position. Methods and materials Twelve patients with lung cancer who had AT and 10 patients without AT underwent repeated 4-dimensional fan beam computed tomography (CT) scans during radiation therapy per protocols that were approved by the institutional review board. Interfraction volume changes of AT and PT were correlated with PT displacements relative to bony anatomy using both a bounding box (BB) method and change in center of mass (COM). Linear regression modeling was used to determine whether PT and AT volume changes were independently associated with PT displacement. PT displacement was compared between patients with and without AT. Results The mean initial AT volume on the planning CT was 189 cm3 (37-513 cm3), and the mean PT volume was 93 cm3 (12-176 cm3). During radiation therapy, AT and PT volumes decreased on average 136.7 cm3 (20-369 cm3) for AT and 40 cm3 (−7 to 131 cm3) for PT. Eighty-three percent of patients with AT had at least one unidirectional PT shift that was greater than 0.5 cm outside of the initial BB during treatment. In patients with AT, the maximum PT COM shift was ≥0.5 cm in all patients and \u3e1 cm in 58% of patients (0.5-2.4 cm). Changes in PT and AT volumes were independently associated with PT displacement (P \u3c .01), and the correlation was smaller with COM (R2 = 0.58) compared with the BB method (R2 = 0.80). The median root mean squared PT displacement with the BB method was significantly less for patients without AT (0.45 cm) compared with those with AT (0.8cm, P = .002). Conclusions Changes in AT and PT volumes during radiation treatment were significantly associated with PT displacements that often exceeded standard setup margins. Repeated 3-dimensional imaging is recommended in patients with AT to evaluate for PT displacements during treatment. Summary This study analyzed 12 patients with atelectasis and 10 patients without atelectasis who underwent repeat 4-dimensional fan beam computed tomography during radiation therapy. Patients with atelectasis had significantly greater tumor displacements than patients without atelectasis, and these tumor displacements often exceeded standard setup margins. Patients with atelectasis may benefit from repeated 3-dimensional imaging during radiation therapy and possible replanning for large tumor displacements