### Table 1: Parameters of grains and ambient medium adopted in this paper.

"... In PAGE 4: ... The uctuating torque Lz spins up grains to an rms angular velocity h!2i1=2 = hL2 zi1=2 td Iz tL tL + td 1=2 ; (3) (Purcell 1979), where Iz = 8 3 sa5r4 is the z component of the momentum of inertia, td is the rotational damping time (see Appendix A) td = 2r (r + 2) a%s nHmHvH 1 (1:2 ? 0:292y) ; (4) and tL is the lifetime of an active site. To obtain both characteristic numerical values and functional dependencies we will use quantities normalized by their standard values (see Table1 ). We denote the normalized values by symbols with hats, e.... ..."

### Table 2. Parameters of the simulated shock-cloud interactions.

2006

"... In PAGE 2: ... 1). Table2 summarizes the physical parameters characterizing the simulations, namely the shock Mach number, M, the density contrast between the cloud and the ambient medium, = ncl=nism, the velocity of the SNR shock, w, the temperature and density of the post-shock ambi- ent medium, Tpsh and npsh respectively, and the cloud crushing time, cc, i.e.... ..."

### Table 1: ATMI boundary conditions

2006

"... In PAGE 2: ... The conductance h2 between the copper layer and the ambient medium is computed as h2 = 1=(RhsL2), where Rhs is the heat sink thermal resistance and L is the heat sink width. Boundary conditions are listed in Table1 , where T1 and T2 are the temperatures in layers 1 and 2 respectively, and q(x;y; t) is the surface power density. The ff3d model is depicted on Figure 2.... ..."

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### Table 1. Approximate Formulae for a SNR Expanding in a Strati ed Medium

"... In PAGE 4: ...elationship as in the 1D Sedov solution (see e.g. Bisnovatyi-Kogan amp; Silich 1995) PS = 4 5 25 E V ; (9) where 5 = 2:025, E is the explosion energy and V = 4 3 ab2 is the volume of the remnant approximated by an ellipsoid. Combining equations (1), (2) and (9), and identifying z = s along the minor axis of the ellipsoid we have e?s=h _ b2 = 4 5 25 E ab2 : (10) After expressing s and b as functions of a, we get da dt = 5=2 5h s E cosh2(a=2h) pa arctansinh(a=2h); (11) which, after integrating gives t(a) = ?5=2 E ?1=2 (2h)5=2 I(a=2h) t2h I(a=2h); (12) where t2h is the nominal time at which a Sedov remnant in a homogeneous medium would reach a radius of 2h, and the integral I(x) is de ned in Table1 for numerical evaluation. The numerical form of t2h is t2h = 17:32 yr (2hpc)5=2 n1=2 =E1=2 51 (13) where hpc is h in parsecs, E51 is E in units of 1051ergs, and n is the nuclear number density of the ambient medium in cm?3.... In PAGE 4: ... After substituting _ a from equation (11), one gets explicit formulae for shock velocities at two density extremes: vH and vL. Obviously, the shock expansion velocity on the equator is the geometrical average of vH and vL | these results are given in Table1 . The ratio of expansion velocities at the two ends is exp(a=h).... In PAGE 5: ... Numerically, the minimum of t + Ct?9=5 occurs at t1 = [9C=5]5=14 such that the rst gas to cool was initially a distance r1 r(t1) = 19:62 pc E2=7 51 =n3=7 (15) from the explosion site, and was shocked at time t1 (see Cox amp; Anderson 1982, Cox 1986). The expression for C can be obtained by substituting equation (2) to (14), and using formulae for the Sedov radius and velocity from Table1 . One can get then C = 1 32 ? p3=5 3 m9=10=( p k) ?E0:6=n1:6 0 .... In PAGE 5: ... Noting that t2h = t1(2h=r1)5=2 yields tcool(a; z) = 5 9 t2h r1 2h 7 exp(5z=2h) (a=2h)3=2(b=2h)3 : (17) A measure of the likehood of nding a remnant with a cold shell only on the dense end is provided by the ratio t? cool=t+ cool of cooling times between the tenuous and dense ends. These cooling times can be obtained by minimizing the value of the sum tcool + t(a) of times given by equations (17) and (12) over x = a=2h t cool = t2h minx I(x) + 5 9( r1 2h)7 g (x) ; (18) where the function g (x) is given in Table1 , and the upper (lower) sign corresponds to the dense (tenuous) end. The formula to derive values of x at minimum, x c , is given in Table 1.... In PAGE 5: ... These cooling times can be obtained by minimizing the value of the sum tcool + t(a) of times given by equations (17) and (12) over x = a=2h t cool = t2h minx I(x) + 5 9( r1 2h)7 g (x) ; (18) where the function g (x) is given in Table 1, and the upper (lower) sign corresponds to the dense (tenuous) end. The formula to derive values of x at minimum, x c , is given in Table1 . One can see that x c is a function of only one variable: r1=2h = (14=9)?2=5rcool=2h.... In PAGE 8: ... Applications to hydrodynamical models and conclusions Assuming that the shock wave propagating in an exponentially strati ed medium takes the shape of an ellipsoid, we were able to nd explicit expressions for its size and expansion velocity as functions of time, and for the cooling time at both ends and on the equator. As presented in Table1 , these expressions take forms similar to the Sedov (1959) solution for a uniform ambient medium. Nevertheless, while the Sedov solution is self-similar, there are no such solutions for nonuniform media.... ..."

### Table 4. Ambient syntax

"... In PAGE 4: ... Ambients can be moved as a whole under the control of agents; these are confined to ambients. The syntax of the calculus is reported in Table4 . Ambient processes use capabilities for control- ling interaction.... ..."

### Table XV. Ambient syntax

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### Table 9: Ambients Syntax

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### Table 12: Ambients Operational Semantics

2005

"... In PAGE 48: ...4.2 Ambients Operational Semantics Ambients processes are executed according to the reduction relation ! defined in Table12 . Like for the previous calculi, ! relates configurations of the form A .... ..."

### Table 4 shows that if the ambient temperature is low, the ambient humidity is high, and the mold

1999