Boltzmannian Statistical Mechanical Foundations of Irreversibility

A dilute gas initially in equilibrium and confined to half of an isolated box by a partition willirreversibly diffuse once the partition is removed. A new equilibrium establishes, and according tothermodynamics, entropy has increased. This paper explores Boltzmann’s work in equilibrium andnonequilibrium statistical mechanics to explain this irreversible process beginning with the underlyingtime symmetric micro-dynamics of the gas particles. Boltzmann’s ergodic hypothesis, transport equation(BE), and H-theorem are examined, as well as the reversibility and recurrence objections to the BE, andtheir resolutions through the statistical explanation of the BE. The entire pursuit is driven by thequestion: “How can one describe macroscopically irreversible phenomena from dynamics which is timereversible and recurring?” A numerical simulation of gas in a partitioned box is developed to illustrate the discussion above.The simulation explicitly calculates the particle distribution function and Boltzmann’s H-function throughtime, and verifies the kinetic and anti-kinetic behavior as expected according to the BE and Loschmidtrespectively. We find that reversibility is unstable under perturbations, which compares with the results ofOrban and Bellemans (1967). This implies that states which are in nonequlibrium, or lead tononequlibrium, are less populated than equilibrium states, as shown by Boltzmann

Giving in Illinois, 2015

Illinois is home to over 5,200 grantmaking foundations spanning all types—independent or family, corporate, community, and operating—sizes, and issue areas. The community includes many foundations that only give locally or within the state, as well as those that fund nationally and even internationally. The following analysis provides an overview of the scale and composition of the Illinois foundation community and an examination of how Illinois foundations have fared relative to U.S. foundations in general over the past decade

Episodic starbursts in dwarf spheroidal galaxies: a simple model

Dwarf galaxies in the Local Group appear to be stripped of their gas within 270 kpc of the host galaxy. Color-magnitude diagrams of these dwarfs, however, show clear evidence of episodic star formation (\Delta{}t ~ a few Gyr) over cosmic time. We present a simple model to account for this behaviour. Residual gas within the weak gravity field of the dwarf experiences dramatic variations in the gas cooling time around the eccentric orbit. This variation is due to two main effects. The azimuthal compression along the orbit leads to an increase in the gas cooling rate of ~([1+\epsilon]/[1-\epsilon])^2. The Galaxy's ionizing field declines as 1/R^2 for R>R_disk although this reaches a floor at R~150 kpc due to the extragalactic UV field ionizing intensity. We predict that episodic SF is mostly characteristic of dwarfs on moderately eccentric orbits (\epsilon>0.2) that do not come too close to the centre (R>R_disk) and do not spend their entire orbit far away from the centre (R>200 kpc). Up to 40% of early infall dwarf spheroidals can be expected to have already had at least one burst since the initial epoch of star formation, and 10% of these dwarf spheriodals experiencing a second burst. Such a model can explain the timing of bursts in the Carina dwarf spheroidal and restrict the orbit of the Fornax dwarf spheroidal. However, this model fails to explain why some dwarfs, such as Ursa Minor, experience no burst post-infall.Comment: 8 pages, 8 figures. ApJ accepte

Ice damage in loblolly pine: Understanding the factors that influence susceptibility.

Abstract: Winter ice storms frequently occur in the southeastern United States and can severely damage softwood plantations. In January 2004, a severe storm deposited approximately 2 cm of ice on an intensively managed 4-year-old loblolly pine (Pinus taeda L.) plantation in South Carolina. Existing irrigation and fertilization treatments presented an opportunity to examine the effects of resource amendments on initial ice damage and subsequent recovery. Fertilized treatments showed more individual stem breakage, whereas non fertilized treatments showed more stem bending; however, the proportion of undamaged trees did not differ between treatments. Irrigation did not influence the type of damage. Trees that experienced breakage during the storm were taller with larger diameter and taper and leaf, branch, and crown biomass compared with unbroken trees. One growing season after ice damage, relative height increases were significantly greater for trees experiencing stem breakage compared with unbroken trees; however, relative diameter increases were significantly lower for these trees. Relative diameter increases for broken trees were smaller for fertilized treatments compared with nonfertilized treatments. A reduction in wood strength was ruled out as the cause of greater breakage in fertilized trees; rather, fertilized trees had reached an intermediate diameter range known to be susceptible to breakage under ice loading

Fertilizer Response Curves for Commercial Southern Forest Species Defined with an Un-Replicated Experimental Design.

There has been recent interest in use of non-replicated regression experimental designs in forestry, as the need for replication in experimental design is burdensome on limited research budgets. We wanted to determine the interacting effects of soil moisture and nutrient availability on the production of various southeastern forest trees (two clones of Populus deltoides, open pollinated Platanus occidentalis, Liquidambar styraciflua and Pinus taeda). Additionally, we required an understanding of the fertilizer response curve. To accomplish both objectives we developed a composite design that includes a core ANOVA approach to consider treatment interactions, with the addition of non-replicated regression plots receiving a range of fertilizer levels for the primary irrigation treatment

Prospectus, May 6, 1974

KAREN COLEMAN ELECTED NEW STU-GO PRES; Gallup Explains Effect Of Polls; Parkland Debate Team Ends Year At Nationals; All Races Close Despite Poor Voter Turnout; Enthusiam Abounds At IOC Spring Carnival; IE Team Winds-Up Season With Good National Showing; Parkland College Foundation Officers Selected At Meeting; Cruisin\u27 \u2774; Letter To The Editor; The Short Circuit; Let\u27s Go To The Bars; IVC New Service Officer, Menaugh; Vet\u27s Corner; Monday\u27s Coach; Cobras Win One, Lose Three In Double-Header; Parkland Athlete Randy Williams Looks Over Schools; I/M Tryouts Now For And Tennis Track, Golf; Amana Commune, A Lifestyle From A Dream; Pulitzer Prize Poet To Appear At Parkland; Library Hours During Exam Week; A Column By and For Women; National Women\u27s Music Festival; Crosswords; Student Raffle; President\u27s Report; Registration Info For Fall, 1974 Available To Students Now; Happy Birthday; Classified Ads; Parkland Players To Present Play; Recycle Paper; Wainwright Captures Audience With Real Life Situations; American Odyssey; Parkland Events; Final Exam Schedule - Spring Quarter, 1973-1974; Sangamon State Representative; Krannert Art Schedulehttps://spark.parkland.edu/prospectus_1974/1013/thumbnail.jp

Prospectus, May 13, 1974

CLASS OF \u2774 COMMENCEMENT; Openhouse Set For May 19; 648 Parkland Students Eligible To Participate; Dr. Winters To Speak At Graduation; Parkland Groups Win Awards At Jazz Fest; StuGo President Offers Welcome; Dental Students Capped At Banquet; The Short Circuit; Letters To The Editor; New Stu-Go Officer; President\u27s Report; Crosswords; Parkland College Student Life; Instructional Programs; Admission: Who may Enroll?; Tuition & Fees; Financial Aid; Counseling; Placement; Veterans; Student Life; Summer Session 1974; Academic Calendar 1974-1975; Semester System Fall 1975; In Campus Design, Parkland: Not Just Another School; No Golden Quill This Quarter; Petitioned and Qualified Candidates Spring Quarter 1973-1974; One-Punch Leads To Death Of UI Student; Movie Projector Reported Missing; A Column By and For Women; A Column By and For Men; Self-Help Clinic Set For Women; Vet\u27s Corner; Field Trip Meeting Set; Pig Guards Pot Plot From Police Raid; Blood Drive; Summer Field Course In American Southwest; P/C Student Wins Distinguished Award; Allerton Day Shows Ecological Benefits Of Park; Debate Team Finishes Best Year Ever; Monday\u27s Coach; Thank You; High-Scoring Henrichs Opts For Parkland Cage Team; Parkland Coaches Review Year; Cobras Bat Way Over .500; P/C Players Thrill Audience; Bartow On His Way; Pritchett Not To Be Outdone; On The Way Out; Classified Ads; End-Of-Year Gala Planned By Phys Ed. Dept.; Social, Religious Traditions Expressed In Roots Afrikana; Jones Cites Improvements In Prospectus; Prospectus Staff Positions Open For New School Year; Business Student Wins Award; Krannert Art Schedule; Many Financial Awards Open To Incoming Parkland Students; Parkland Vets Info Center On Wheelshttps://spark.parkland.edu/prospectus_1974/1012/thumbnail.jp