A statistical mechanics model for free-for-all airplane passenger boarding

I present and discuss a model for the free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of the population of air travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with models which involve assigned seats. This model can also be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results may be of value to industry professionals as a useful description of this boarding method. However, it also has significant value as a pedagogical tool since it is a relatively unusual application of undergraduate level physics and it describes a situation with which many students and faculty may be familiar.Comment: version 1: 4 pages 2 figures version 2: 7 pages with 5 figure

Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Consistent treatment of hydrophobicity in protein lattice models accounts for cold denaturation

The hydrophobic effect stabilizes the native structure of proteins by minimizing the unfavourable interactions between hydrophobic residues and water through the formation of a hydrophobic core. Here we include the entropic and enthalpic contributions of the hydrophobic effect explicitly in an implicit solvent model. This allows us to capture two important effects: a length-scale dependence and a temperature dependence for the solvation of a hydrophobic particle. This consistent treatment of the hydrophobic effect explains cold denaturation and heat capacity measurements of solvated proteins.Comment: Added and corrected references for design procedure in main text (p. 2) and in Supplemental Information (p. 8

Neurogenic Fever after Acute Traumatic Spinal Cord Injury: A Qualitative Systematic Review.

STUDY DESIGN: Systematic review. OBJECTIVE: To determine the incidence, pathogenesis, and clinical outcomes related to neurogenic fevers following traumatic spinal cord injury (SCI). METHODS: A systematic review of the literature was performed on thermodysregulation secondary to acute traumatic SCI in adult patients. A literature search was performed using PubMed (MEDLINE), Cochrane Central Register of Controlled Trials, and Scopus. Using strict inclusion and exclusion criteria, seven relevant articles were obtained. RESULTS: The incidence of fever of all origins (both known and unknown) after SCI ranged from 22.5 to 71.7% with a mean incidence of 50.6% and a median incidence of 50.0%. The incidence of fever of unknown origin (neurogenic fever) ranged from 2.6 to 27.8% with a mean incidence of 8.0% and a median incidence of 4.7%. Cervical and thoracic spinal injuries were more commonly associated with fever than lumbar injuries. In addition, complete injuries had a higher incidence of fever than incomplete injuries. The pathogenesis of neurogenic fever after acute SCI is not thoroughly understood. CONCLUSION: Neurogenic fevers are relatively common following an acute SCI; however, there is little in the scientific literature to help physicians prevent or treat this condition. The paucity of research underscored by this review demonstrates the need for further studies with larger sample sizes, focusing on incidence rate, clinical outcomes, and pathogenesis of neurogenic fever following acute traumatic SCI

Two-mirror Schwarzschild aplanats. Basic relations

It is shown that the theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 leads to the unified description both the prefocal and the postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at fast focal ratio of the system.Comment: 19 page

A purely reflective large wide-field telescope

Two versions of a fast, purely reflective Paul-Baker type telescope are discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25 focal ratio. The first version is based on a common, even asphere type of surface with zero conic constant. The primary and tertiary mirrors are 6th order aspheres, while the secondary mirror is an 8th order asphere (referred to here for brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5 mcm). The second version of the telescope is based on a polysag surface type which uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 + a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface. This approach results in somewhat better images, with D_80 ranging from 0''.16 to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat field, and f/1.25 focal ratio featuring near-diffraction-limited image quality is also presented.Comment: 14 pages, 6 figures; new examples adde

Helium-3 and Helium-4 acceleration by high power laser pulses for hadron therapy

The laser driven acceleration of ions is considered a promising candidate for an ion source for hadron therapy of oncological diseases. Though proton and carbon ion sources are conventionally used for therapy, other light ions can also be utilized. Whereas carbon ions require 400 MeV per nucleon to reach the same penetration depth as 250 MeV protons, helium ions require only 250 MeV per nucleon, which is the lowest energy per nucleon among the light ions. This fact along with the larger biological damage to cancer cells achieved by helium ions, than that by protons, makes this species an interesting candidate for the laser driven ion source. Two mechanisms (Magnetic Vortex Acceleration and hole-boring Radiation Pressure Acceleration) of PW-class laser driven ion acceleration from liquid and gaseous helium targets are studied with the goal of producing 250 MeV per nucleon helium ion beams that meet the hadron therapy requirements. We show that He3 ions, having almost the same penetration depth as He4 with the same energy per nucleon, require less laser power to be accelerated to the required energy for the hadron therapy.Comment: 8 pages, 3 figures, 1 tabl

Making Sense of the Legendre Transform

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure

Mutational Analysis of the Rotavirus NSP4 Enterotoxic Domain that Binds to Caveolin-1

Background: Rotavirus (RV) nonstructural protein 4 (NSP4) is the first described viral enterotoxin, which induces early secretory diarrhea in neonatal rodents. Our previous data show a direct interaction between RV NSP4 and the structural protein of caveolae, caveolin-1 (cav-1), in yeast and mammalian cells. The binding site of cav-1 mapped to the NSP4 amphipathic helix, and led us to examine which helical face was responsible for the interaction. Methods: A panel of NSP4 mutants were prepared and tested for binding to cav-1 by yeast two hybrid and direct binding assays. The charged residues of the NSP4 amphipathic helix were changed to alanine (NSP446-175-ala6); and three residues in the hydrophobic face were altered to charged amino acids (NSP446-175-HydroMut). In total, twelve mutants of NSP4 were generated to define the cav-1 binding site. Synthetic peptides corresponding to the hydrophobic and charged faces of NSP4 were examined for structural changes by circular dichroism (CD) and diarrhea induction by a neonatal mouse study. Results: Mutations of the hydrophilic face (NSP446-175-Ala6) bound cav-1 akin to wild type NSP4. In contrast, disruption of the hydrophobic face (NSP446-175-HydroMut) failed to bind cav-1. These data suggest NSP4 and cav-1 associate via a hydrophobic interaction. Analyses of mutant synthetic peptides in which the hydrophobic residues in the enterotoxic domain of NSP4 were altered suggested a critical hydrophobic residue. Both NSP4HydroMut112-140, that contains three charged amino acids (aa113, 124, 131) changed from the original hydrophobic residues and NSP4AlaAcidic112-140 that contained three alanine residues substituted for negatively charged (aa114, 125, 132) amino acids failed to induce diarrhea. Whereas peptides NSP4wild type 112 −140 and NSP4AlaBasic112-140 that contained three alanine substituted for positively charged (aa115, 119, 133) amino acids, induced diarrhea. Conclusions: These data show that the cav-1 binding domain is within the hydrophobic face of the NSP4 amphipathic helix. The integrity of the helical structure is important for both cav-1 binding and diarrhea induction implying a connection between NSP4 functional and binding activities