sets: Cross section data sets: transparent and interchangeable Final state calculation: Final state calculation: models by **particle**, energy, material Electromagnetic Physics Hadronic physics Maria Grazia Pia, INFN Genova Interface to external tools no dependence/Oncological Regional Center 2 LIP - Lisbon Central-Axis depth dose **curve** for a 10x10 cm2 field **size**, compared with experimental data (ionisation chamber ) Validation of phase-space **distributions** from a Siemens KD2 linear accelerator at 6 MV photon /

the star to gradually grow in **size**, passing through the subgiant stage until/ relativitymassevent horizonblack bodyquantum field theory in **curved** spacetimeHawking radiationthe same spectrumblack holes of /**distribution** of hot gas in galaxies and clusters of galaxies, and more recently the pattern of anisotropies in the cosmic microwave background. According to consensus among cosmologists, dark matter is composed primarily of a not yet characterized type of subatomic **particle**. The search for this **particle**/

in the classification of soils. Effective **size**, D 10 : The **size** such that 10% of the **particles** are smaller than that **size**. D 60 : The **size** such that 60% of the **particles** are smaller than that **size**. D 30 : The **size** such that 30% of the **particles** are smaller than that **size**. 18 19 Parameters Obtained From Grain **Size** **Distribution** **Curve**: 1- Uniformity Coefficient Cu (measure of the **particle** **size** range) C u = D 60/

is a constant chosen to give a test of the desired **size**. Equivalently, optimal scalar test statistic is N.B. any monotonic/2 nd ed., Wiley, 2002. Ilya Narsky and Frank C. Porter, Statistical Analysis Techniques in **Particle** Physics, Wiley, 2014. 朱永生 （编著），实验数据多元统计分析， 科学出版社 ， 北京， 2009 。 G. Cowan Weizmann Statistics Workshop/**curve** is better; usually analysis focused on a small part of the **curve**. G. Cowan Weizmann Statistics Workshop, 2015 / GDC Lecture 2page 88 2D Example: discussion Even though the **distribution**/

LS-SIMat11 Dispersion **Curves** Propagation **curve** in 1 (dielectric medium) does not cross the surface plasmon dispersion **curve** U NIVERSITA DEGLI /adsorbates e.g. biomolecules. Surface plasmon changes with **particle** **size**. Surface plasmon changes with **particle** shape. Single Electron Effects: Coulomb Blockade. U /**size** **distributions** must be very narrow. The growth kinetics must be carefully controlled. Quantum **Size** Effect produces Artificial Atoms U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat38 **Size**/

Chan, T. P. , and R. S. Govindaraju. 2004 Chan, T.P., and R.S. Govindaraju. 2004. Estimating soil water retention **curve** from **particle**-**size** **distribution** data based on polydisperse sphere systems. Vadose Zone J. 3:1443-1454. The measured and estimated soil water retention **curves** of Troup loamy sand (code no. 1012) (a) with fitted α and (b) with theoretical α. The fitted α value is higher than/

clays Sedimentation test Rate at which **particles** settle Strokes law states –that **particles** in a suspension settle out at a rate that varies with their **size** Plasticity – to measure grain types Grain **Size** **Distribution** **Curve** Used to help describe and classify a soil Shape – Uniform soil –**curve** a on page 19 Well graded – **curve** b on page 19 Effective **size** 10% **size** is considered effective **size** – page 19 – sample b.09mm/

/ D10 Cc Gradation coeff. = (D30 )2/ (D60 * D10 ) 11/16 **PARTICLE**-**SIZE** ANALYSIS ASTM D 422 12/16 13/16 **PARTICLE**-**SIZE** ANALYSIS ASTM D 422 14/16 **PARTICLE**-**SIZE** ANALYSIS ASTM D 422 15/16 16/16 Pharos University Faculty of Engineering CV 256: Soil/2244523.5 * Determine the percent finer than each sieve and plot a Grain -**Size** **Distribution** **Curve** for all the samples. * Calculate D 10, D 30 & D 60 form the Grain - **Size** **Distribution** **Curve** for all the samples * Calculate the uniformity coefficient, C u * Calculate the /

**size** of **particles** generated by grinding, milling and crushing operations, the 2-Parameter Weibull **distribution** is used, and in these applications it is sometimes known as the Rosin-Rammler **distribution**. (In this context it predicts fewer fine **particles** than the Log-normal **distribution** and it is generally most accurate for narrow **particle** **size** **distributions**/a good idea to make the primitive plot we started out and decide what other **curves** might “reasonably” be drawn to the data. This will give you a rough /

r=0, preventing **particles** from reaching the singularity at r=0. Geodesically complete spacetime. /**curves** become the Kepler-Newtonian **curves** at large distances from the galaxies (satellites). For every feature in the surface brightness **distribution**, MOG produces a corresponding feature in the predicted rotation **curve** (matching the observed rotation **curve**/oscillations may become observable as the galaxy surveys increase in **size** and the window functions narrow in **size**. 31 5. MOG Verifiable Predictions The matter power /

al 2001 Flatter beam attenuation spectra (small γ ) implies flatter **particle** **size** **distribution** (small ) (2) Assuming spherical non- absorbing **particles** c p (λ) is described well as a power law function of wavelength (λ) c p (λ) ~ λ -γ γ ≈ - 3 Relationship between optical properties **size** b bp /Volume b p /Volume b sp /Mass All **curves** are ‘resonant’ **curves** Highest sensitivity for micron **sized** **particles** **Size** of max response varies 1/D D3D3 Instruments are consistent/

number u uniformly **distributed** between 0 and f max, i.e. (3) If u < f (x), then accept x. If not, reject x and repeat. G. Cowan Statistical Methods in **Particle** Physics44 Example with acceptance-rejection method If dot below **curve**, use x /1/2. G. Cowan Statistical Methods in **Particle** Physics56 Example of variance by graphical method ML example with exponential: Not quite parabolic ln L since finite sample **size** (n = 50). G. Cowan Statistical Methods in **Particle** Physics57 The method of least squares Suppose we /

. G. Cowan iSTEP 2015, Jinan / Statistics for **Particle** Physics / Lecture 211 Classification viewed as a statistical test Probability to reject H 0 if true (type I error): α = **size** of test, significance level, false discovery rate Probability to/) versus signal efficiency ε s. Higher **curve** is better; usually analysis focused on a small part of the **curve**. G. Cowan iSTEP 2015, Jinan / Statistics for **Particle** Physics / Lecture 2page 68 2D Example: discussion Even though the **distribution** of x 2 is same for signal/

are falling at a constant rate. The pipette method (Andreasen) Sedimentation methods may be used over a **size** range from 1-200 microns to obtain a **size**- weight **distribution** **curve** and to permit calculation of the **particle** **size**. The pipette method (Andreasen) is the simplest means of incremental **particle** **size** analysis. A 1% suspension of the powder in a suitable liquid medium is placed in the pipette. At/

the covariances of the original variables. Limitations: exact only iflinear. Approximation breaks down if function nonlinear over a region comparable in **size** to the i. N.B. We have said nothing about the exact pdf of the x i, e.g., /**curve**, use x value in histogram. G. Cowan Aachen 2014 / Statistics for **Particle** Physics, Lecture 157 Improving efficiency of the acceptance-rejection method The fraction of accepted points is equal to the fraction of the box’s area under the **curve**. For very peaked **distributions**/

2015 1 Some Developments in Statistical Methods for **Particle** Physics **Particle** Physics Seminar IHEP, Beijing 19 August, 2015/ IHEP seminar / 19 August 2015 5 Confidence interval from inversion of a test Carry out a test of **size** α for all values of μ. The values that are not rejected constitute a confidence interval for μ at/ ε s. Higher **curve** is better; usually analysis focused on a small part of the **curve**. G. Cowan IHEP seminar / 19 August 2015 57 2D Example: discussion Even though the **distribution** of x 2 is/

recorder which indicates stage versus time and is then transformed to a discharge hydrograph by application of a rating **curve**. Hydrograph Analysis Contd. Components of Hydrograph Components of Hydrograph A hydrograph has 4 components: 1). Direct surface / Values of specific yield depend upon the soil **particle** **size**, shape and **distribution** of pores and degree of compaction of the soil. Values of specific yield depend upon the soil **particle** **size**, shape and **distribution** of pores and degree of compaction of the/

N-P likelihood-ratio test outperforms others in the figure [James 2006] – reason is N-P lemma As data **size** increases, power **curve** becomes closer to step function The power of a test usually also depends on the parameter of interest: different methods may/The **distribution** of residuals of 306 measurements in [20] x1000! Eye fitting: Sensitivity to bumps I will discuss the quantification of a signal’s significance later on. For now, let us only deal with our perception of it. In our daily job as **particle** /

his coworker interpreted the plot of specific surface area vs. compressional force. Armstrong and coworkers described similar **curves**, at higher compressional forces (dotted lines) some materials shows increase in specific surface area due to lamination of/flow properties of the bulk material with individual granule strength and porosity. **Particle** shape and **size** **distribution** are important factors in packing and flow. **Particles** of more regular shape (nearly spherical) have low angles of response and high/

tend to get information about a ~ λ Evolution of **size** **distribution** dN(a)/dt = -rate of destruction + rate of production of bodies with radius a Larger **particles** destroyed by collisions create smaller **particles** Smallest **particles** can be removed or destroyed by drag, blowout, /not precisely known Complications As Q * D depends on sizescale. Refinements include taking this into account -> A **curve** or two power laws instead of one Actually Q parameter is perhaps only a poor approximation of real parameters/

Photoabsorption cross section of medium Density & refractive index Incident **particle** momentum, P Incident **particle** mass (muon) Overview Input theory Maxwell’s equations Causality/which is well known and includes the finite proton **size** as well (see Perkins, 3rd edn.). Nuclear/1 vs. log 10 P where P is muon momentum **Curve** = Bethe Bloch with Mean Ionisation Potential = 18.59eV/ respectively. 3.Statistical effects remain slippery to handle. **Distributions** of variables, not their simple means and standard deviations/

impedance are proportional to the volume of **particles**. Measurement range of 0.6 to 1200mm. **Particle**-**Size** Diagram **Particle** **size** **distribution** (PSD) is often expressed as **particle** diameter as a function of soil mass fraction of smaller **particles**. The **curve** is equivalent to cumulative statistical **distribution** of **particle** diameters in the sample (note log scale for **particle** **sizes**). Comparison of methods for PS analyses Six methods for **particle** **size** analysis were compared in recent study/

that for large **particles** all **distribution** coincide and are therfore not dependent on optical properties. The red **curve** has the wron refractive index and shows some departure to the blue correct **curve**. The green **curve** has been generated by/2% 0.5 - 2% Users Sampling Sample Handling Units 1 - 2% Optical Bench 0.5 - 2% Characterising **distributions** A **particle** **size** **distribution** contains a large amount of data. To assist comparisons and examination we extract simpler quantities from the data known as averages /

from right to left, f ines to right, coarse to left Graphically represent grain **size** **distribution** –mean grain **size** –standard deviation from a normal **distribution** (sorting) –symmetry (skewness) –flatness of **curve** (kurtosis) Describing Siliciclastics Grain **size** analysis- graphic analysis Different depositional environments exhibit different grain **size** **distributions** Glacial sediments poorly sorted River sediments moderately sorted Beach sediments well sorted Statistical/Graphic Presentation of Texture/

by quantising textures applied to geometry from truecolor to lower bit **size** samples Or, can quantise the values generated by normal lighting techniques/ sparks, fireworks etc. Colour and visibility attenuates over time **Curves** – for plants, render entire temporal existence of **particle** as stems Textured Quads – for smoke, flames, blood plant/CRICOS No. 000213J a university for the world real R Bidirectional Surface Scattering **Distribution** Function The BSSRDF, S, relates the outgoing radiance L o, at the/

**size** range of soil **particles**, expressed as a percentage of total dry weight. The **particle** **size** **distribution** of soil can be fined by two methods. • The sieve analysis technique is applicable for soil grains larger than No. 200 (0.075 mm) sieve **size**/.5 * Determine the percent finer than each sieve and plot a Grain -**Size** **Distribution** **Curve** for all the samples. * Calculate D10, D30 & D60 form the Grain -**Size** **Distribution** **Curve** for all the samples * Calculate the uniformity coefficient, Cu * Calculate the /

, the scattered wave frequency at a given angle should be a **distribution** of Doppler- shifted values Compton Effect, Observations Compton’s experiments showed/**particles** In this model, entities have both **particle** and wave characteristics We much choose one appropriate behavior in order to understand a particular phenomenon Ideal **Particle** vs. Ideal Wave An ideal **particle** has zero **size**/ well is the upward-facing region of the **curve** in a potential energy diagram The **particle** in a box is sometimes said to be /

event represents p p Reasonably stable **particles** “charged **particles**” (with energy measured by magnetic field), “neutral **particles**” (with energy measured in a calorimeter / events in them The red **curve** is naïve expected number of events in each bin – Normal **distribution** Good but not perfect as /**curve** and 250 is expected number of events with an error of √250 ≈ 16 The one sigma line runs from 250- √250 to 250 + √250 The plots get rough if reduce number of events from 40000 to 400 or 4000 Use larger bin **size**/

**Curve** CHEMICAL REACTION ENGINEERING LABORATORY Gas Liquid Studies in Stirred Tank Reactor New techniques in CT implementation result in better reconstruction!!! How ??? Cross sectional gas holdup **distributions**/ REACTION ENGINEERING LABORATORY bubble dynamics, i.e. bubble **size** **distribution**, bubble velocity **distribution**, specific interfacial area and gas holdup are among the key/The Present Work To demonstrate the ability of single **particle** CARPT technique to visualize 3D flow patterns inside a simulated/

50 % probability limit we can see that the probable error is given by pe = 0.6745 . Comparison of Gaussian and Poisson **Distributions** A comparison of the Poisson and Gaussian **curves** reveals the nature of the Poisson **distribution**. It is the appropriate **distribution** for describing experiments in which the possible values of the data are strictly bounded on one side but not on the other/

: 3D: The vector form Position of the **particle**: M = mass of the object object System of **particles**: Position COM: Solid bodies: Continuous **distribution** of matter. **Particles** = dm (differential mass elements). 3D: M/m 1 = 0.500 kg is released from rest at the top of a **curve**-shaped frictionless wedge of mass m 2 = 3.00 kg, which sits on/ (a) Thrust (b) Model rocket engines are **sized** by thrust, thrust duration, and total impulse, among other characteristics. A **size** C5 model rocket engine has an average thrust of 5/

the genes are translated into protein from an RNA strand complementary to that of the genome (as packaged in the virus **particle**). There are some plant viruses in this group and it also includes the viruses that cause measles, influenza and rabies./papaya. **DISTRIBUTION**: Where papaya is grown. 10 TRANSMISSION: White fly, Bemissia tabacci. SYMPTOMS: Almost all the leaves of the plant are reduced in **size** and show malformation and sever curling, crinkling and distortion. The margins of the leaves are **curved** or /

. Thus, we need an estimate of the **size** range present and the number or weight fraction of each **particle** **size**. This is the **particle**-**size** **distribution** and from it we can calculate an average **particle** **size** for the sample. **Particle** **Size** **Distribution** When the number or weight of **particles** lying within a certain **size** range is plotted against the **size** range or mean **particle** **size**, a so-called frequency **distribution** **curve** is obtained. This is important because it/

pairs j=i,l with σ in a compact set) dσ ΩdN 2 ΩdN x Sd-1 Introducing a one-**particle** **distribution** function (by setting v1 = v) and the hierarchy reduction for B= -∞ or B=0 B B B The / where self-similar asymptotics is possible: M , M whose spectral function is Where μ(p) is a **curve** with a unique minima at p0>1 and approaches + ∞ as p 0 and μ’(1) < 0/ next two pages: Mean free path l0 = 1. Number of Fourier modes N = 243, Spatial mesh **size** Δx = 0.01 l0 . Time step Δt = r mft Sudden heating problem (BGK eq. with/

roof must be protected from the weather and emissions from ducting and chimneys **Distribution** **Distribution** Ring main installation Dead leg with a drip leg drain on each corner to/ Relieving G1/4 Spring range 0-10 bar Primary pressure 10 bar The **curves** show the characteristics and hysteresis of pressure from a set value for increasing /cylinders etc. Oil drips are broken up in the main air stream and all **particle** **sizes** carried in the air Drip rate is adjustable Oil fog lubricator Oil drips visible through/

assumed rules lead (formally, under additional assumptions) to molecular chaos, that is Introducing a one-**particle** **distribution** function (by setting v 1 = v) and the hierarchy reduction The corresponding “weak formulation/being under discussion where self-similar asymptotics is possible, M Where μ(p) is a **curve** with a unique minima at p 0 >1 and approaches + ∞ as p / simplest setting: N= Number of Fourier modes in each j-direction in 3D Spatial mesh **size** Δx = O.O1 mfp Time step Δt = r mft, mft= reference time/

- in the galactic plane - with radii - with overall **size** consistent with tidal torque theory 5.The evidence for caustic rings / 5 states 316 251 system states Start with Number of **particles** Total energy Thermal averages Integrate Calculate Do the approach the on/of dark matter (A. Natarajan and P.S. ’07) Rotation **curve** of Andromeda Galaxy from L. Chemin, C. Carignan & T./ et al. 1979, 1987from caustic rings The specific angular momentum **distribution** on the turnaround sphere Is it plausible in the context of/

gives a 3d version of previous AV model In all **particle** simulations, accuracy requires frequent and accurate regridding « classical » interpolation formulas Error **curves** random initquiet start init with remeshing Typical example showing importance of/ designed for FD Global mapping approach: **Particle** grid Vorticity contours Measure of accuracy/cost: enstrophy profiles and number of **particles** compared to uniform **size** **particles** Dotted line: uniform **particle** **distribution** AMR approach: Conclusion : 1.About/

-sieving procedure (section 4.6.4) should be followed for all soils (Head, 1992). (Head, 1992) Sieve analysis Hydrometer analysis 2.2 Grain **Size** **Distribution** (Cont.) Finer Effective **size** (D10): This parameter is the diameter in the **particle**-**size** **distribution** **curve** corresponding to 10% finer. The effective **size** of a granular soil is a good measure to estimate the hydraulic conductivity an ddrainage through soils. Log scale Effective/

43% 29% 41% Lung Deposition Measurements RESPI instrument RESPI **Particle** Lung Deposition Validation of the **Particle** Lung Deposition Determined by the dry **size** **distribution** and the hygroscopic properties. H-TDMA Hygroscopic Tandem Differential Mobility Analyzer Water uptake of individualparticles Humidified **particle** **size** **distribution** **Particle** Lung Deposition Modelled Measured DMPS Differential Mobility **Particle** **Size** Dry **particle** **size** **distribution** DMPS – huvud saken H-TDMA – elle ranna kemiska bestämning/

good idea for an unknown material). **Particle** **size** **distribution** Most spherical nanoparticle **size** **distributions** are fit well by the log normal **distribution** (slightly asymmetric): Y=A*exp(-0.5(log(R)-log(R o )) 2 /b 2 ) –Two parameters b (the width of the **distribution**) and R o (the average radius). A is set by the fact that the area under the **curve** is 1. Two types of/

balls There is a lot of empty space between the gas **particles** compared to the **size** of the **particles**. © 2014 Pearson Education, Inc. Kinetic Molecular Theory (basic postulates) The **size** of a **particle** is negligibly small. Under normal pressures, the space between atoms or/attractions we get the following equation. Used for real gases © 2014 Pearson Education, Inc. Real Gases It reveals a **curve** that shows the PV/RT ratio for a real gas is generally lower than ideal for “low” pressures—meaning that the /

two ways: radiative and non-radiative Band gap of spherical **particles** The average **particle** **size** in suspension can be obtained from the absorption onset using / coherent. Balance surface energy against elastic energy. Control of self-assembly? Average **size** & **size** **distribution**. –Affects emission wavelength and sharpness. Density. –Affects gain of QD laser./**size** and density fixed by AFM). Composition is 100% In for the top **curve**, then 80%, 60%, 40% and 20%. Simulations of linear composition gradient QDs (**curves**/

radioactive **particles** passing through a counter in 1 millisecond is 4. What is the probability that 6 **particles** enter the counter in any given millisecond? Using the Poisson **distribution** function/Reddy45 Chap 2-Data Analysis-Reddy46 Table A3. The standard normal **distribution** (cumulative z **curve** areas) Example 2.4.9. Graphical interpretation of probability using the/Reddy67 Chap 2-Data Analysis-Reddy68 portion of **size** 2 2.5.2 Application to discrete probability **distributions** Example 2.5.3. Using the Bayesian /

Range of analysis:- TEM :– 0.001 – 0.1 micron S E M :– 0.01 – 1000 micron Light microscope :- 1 – 1000 micron Light microscope :- Two dimensional image No of **particle** count for draw **size** **distribution** **curve** ( **particle** **size** v/s freq ) Alternative technique Two Technique (1) Scanning Electron Microscopy (SEM) (2) Transmission Electron Microscopy (TEM) SEM give three dimensional image. It has more resolution power then Light/

W. Weyrather et al. RBE depends on Ion Species RBE maximum is shifted to higher LET for heavier **particles** The shift corresponds to a shift to higher energies ~1 MeV/u ~15 MeV/u Why Carbon Ions?/ Parameters Radial Dose **Distribution**: Monte-Carlo (M. Krämer), Analytical Models (Katz, Kiefer), Experimental Data X-ray Survival **Curves**: Experimental data according to LQ; additional assumption: Transition from shoulder to exponential shape at high doses Target **Size** (Nuclear **Size**): Experimental Data Algorithms/

of nanometer **sized** **particles** in living cells Michael Edetsberger Max F. Perutz Laboratories, Department for Biomolecular Structural Chemistry, University of Vienna Introduction Nanoparticles are extensively used in biotechnology and medicine Nanoparticles originated from industrial or combustion processes Nanoparticles play an important role in environmental biology, job safety and medicine Standard techniques Microscopy (Fluorescence, Laser Scanning) Good spatial **distribution** Diffraction/

deviation (SD) and V Total the total volume. Fig. 1-1 Volume **size** **distributions** (in 50 channels on logarithmic scale) of microparticles in low- and high concentration samples (black **curves**) from the Muztagata and Dunde ice cores. Only the high concentration samples obey the log-normal **distribution** (fitted by red **curves**). Only **particles** of 1–30μm diameter were measured. 1. Only high-concentration samples obey/

equation Time-temperature superposition Mechanical models of viscoelastic behaviour Typical stress-strain **curves** for polymers in solid state Polymer dissolution Fractionation Gas permeation Polymer /to determine: –the molar mass, the **particle** **size**, the **particle** density and interaction parameters like virial coefficients and association constants –determination of the molar mass **distribution**, the **particle** **size** **distribution** and the **particle** density **distribution** is also possible The density gradient method /

Now invert the test to define a confidence interval as: set of values that would not be rejected in a test of **size** (confidence level is 1 ). The interval will cover the true value of with probability ≥ 1 . Equivalently,/determine the **distribution** of upper limits μ up one would obtain under the hypothesis of μ = 0. The dashed **curve** is the median μ up, and the green (yellow) bands give the ± 1σ (2σ) regions of this **distribution**. G. Cowan Invisibles 2014 / Statistics for **Particle** Physics92 Choice /

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