% The paper is in plain TeX and it can be % TeXed directly as provided. No input files, % etc., are needed. % Six PostScript figure files are appended. The files are separated % by lines %%============================(information)============. % These can be easily found by searching for ==( . %%======================(the TeX file begins here)=================== \def\NI{\noindent} \def\PPP{\partial} \long\def\UN#1{$\underline{{\vphantom{\hbox{#1}}}\smash{\hbox{#1}}}$} \magnification=\magstep 1 \overfullrule=0pt \hfuzz=16pt \voffset=0.0 true in \vsize=8.8 true in \def\NP{\vfil\eject} \baselineskip 20pt \parskip 6pt \hoffset=0.1 true in \hsize=6.3 true in \nopagenumbers \pageno=1 \footline={\hfil -- {\folio} -- \hfil} \centerline{\UN{\bf Locally Frozen Defects in Random Sequential}} \centerline{\UN{\bf Adsorption with Diffusional Relaxation}} \vskip 0.4in \centerline{\bf Jian--Sheng Wang{\rm ,}$^{a,b}$\ Peter Nielaba$^c$\ {\rm and}\ Vladimir Privman$^d$} \vskip 0.2in \NI\hang $^a${\sl Department of Physics, Hong Kong Baptist College, 224 Waterloo Road, Kowloon, Hong Kong} \NI\hang $^b${\sl Present address: c/o Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511} \NI\hang $^c${\sl Institut f\"ur Physik, Universit\"at Mainz, Staudingerweg 7, D--55099 Mainz, Germany} \NI\hang $^d${\sl Department of Physics, Clarkson University, Potsdam, New York 13699--5820, USA} \vskip 0.4in \centerline{\bf ABSTRACT} Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation allows the deposition process to reach full coverage. The coverage approaches the full occupation value, 1, as a power-law with convergence exponent near $1 \over 2$. For a periodic lattice of finite (even) size $L$, the final state is a frozen random rectangular grid of domain walls connecting single-site defects. The domain sizes saturate at $\sim L^{0.8}$. Prior to saturation, i.e., asymptotically for infinite lattice, the domain growth is power-law with growth exponent near, or possibly somewhat smaller than, $1 \over 2$. \vfill \NI {\bf PACS numbers:}$\;$ 68.10.Jy, 02.50.+s, 82.65.-i \NP \NI \UN{\bf 1.~Introduction} \ Random sequential adsorption (RSA) models have been studied extensively due to their relevance to surface deposition [1-2]. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. In monolayer deposition of colloidal particles and macromolecules [3-6] one can further assume that the adhesion process is irreversible. However, recent experiments on protein adhesion at surfaces [7-8] indicate that in biomolecular systems effects of surface relaxation, due to diffusional rearrangement of particles, are observable on time scales of the deposition process. The resulting large-time coverage is denser than in irreversible RSA and in fact it is experimentally comparable to the fully packed (i.e., locally semi-crystalline) particle arrangement. Irreversible RSA has been studied extensively by many authors [1-2]. The most interesting aspect of such processes is the power-law large-time convergence to the jamming coverage in continuum off-lattice deposition. This slow time-dependence, as opposed to exponential convergence in lattice deposition, is due to gaps arbitrary close in size (and shape) to that of the depositing particles and therefore reached with low probability. Asymptotic arguments describe this rare-event dominated process [9-10]. Crossover from lattice to continuum can be also elucidated analytically [11]. Studies of RSA with added diffusional relaxation by analytical means encounter several difficulties associated with collective effects in hard-core particle systems at high densities (such as, for instance, phase separation), and with the possibility, in certain lattice models, of locally ``gridlocked'' vacant sites. Both complications are not present in $1d$: there are no equilibrium phase transitions (in models without deposition), traces of which might manifest themselves as collective effects in $d>1$ RSA with diffusion [12], and furthermore diffusional relaxation leads to simple hopping-diffusion interpretation of the motion of vacant sites in $1d$ which recombine to form larger open voids accessible to deposition attempts. Thus, both extensive numerical studies and their analytical interpretation were possible in $1d$ [13-15]. For $d>1$ models, a low-density-expansion approximation scheme was applied [16] to off-lattice deposition of circles on a plane, accompanied by diffusional relaxation. However, no analytical studies were reported of the high-density behavior and the associated collective effects. Extensive numerical simulations were reported [12], of the RSA process with diffusional relaxation, for the lattice hard-square model [17], i.e., the square-lattice hard-core model with nearest-neighbor exclusion. This model is well studied for its equilibrium phase transition [17] which is second-order with disordered phase at low densities and two coexisting ordered phases, corresponding to two different sublattice particle arrangements, at high densities. Another simplifying feature of the hard-square model is that the only possible gridlocked (locally frozen) vacancies are parts of domain walls [12]. As a result the coverage reaches the full crystalline limit at large times, by a process of diffusional domain wall motion leading to cluster growth reminiscent of spinodal decomposition in quenched binary alloys and fluids at low temperatures [18-20]. In this work we report extensive computer simulation results for RSA with diffusion on the two-dimensional square lattice with objects occupying two by two squares of four sites. One can view the deposition of such $2\times 2$ objects as equivalent to a hard-core model with nearest-neighbor and next-nearest-neighbor exclusions. The distinctive feature of this model is the existence of locally frozen single-site defects. RSA with diffusion on a periodic lattice then leads to frozen states with domains of four different phases. The corresponding equilibrium ground states are highly degenerate [17,21-22]. The model is detailed in Section~2. The frozen states in the large-time limit are described in Section~3. Time-dependence of the single-site defect density, of the coverage, and of the ordered domain size, are discussed in Sections~4, 5, 6, respectively. These sections also contain discussion of the results. \ \ \NI \UN{\bf 2.~Definition of the Model} \ We consider a square lattice of size $L \times L$, where $L$ is even. Initially all sites are empty. Each trial Monte Carlo step starts with choosing at random a lattice site $(i,j)$. With probability $p$ we try deposition of a two by two square to cover sites $(i,j)$, $(i+1,j)$, $(i,j+1)$, $(i+1,j+1)$. Deposition attempt is successful if these four sites are all empty. The sites are then marked as occupied. In the actual computer program the site $(i,j)$ is further listed as the lower-left corner of a block, for later use. We perform a diffusion attempt with probability $1-p$. Diffusional move is attempted only if the chosen site $(i,j)$ is already one of the lower-left corner sites. We try to diffuse (move) the square in one of the four directions (up, down, left, right) chosen at random, by one lattice spacing. Diffusion is successful if the move is not blocked by other squares. The time $t$ is measured in terms of Monte Carlo steps per site: one time unit is defined as $L^2$ deposition or diffusion attempts (successful or not). In comparing data for different $p$ values, it is further convenient to rescale time by $p$, see [12-14] for details. However, we report specific results only for $p=0.1$ here. Furthermore, all lattice sizes used were powers of 2. This restriction to one $p$ value, and generally the scope of the results presented, were due to numerical difficulties involved in simulating RSA with diffusion in $2d$. For instance, results reported here took over 2 months of CPU time on an HP Apollo Model 720 workstation. However, we checked some of the observations reported in the later sections also for $p=0.8$. The formation of the frozen states on periodic even-sized lattices (Section~3) was also checked for sizes other than powers of 2, and for several $p$ values other than $0.1$. The corresponding equilibrium model has been studied in [17, 21-22]. The equilibrium phase transition from the low-density disordered state to the high-density ordered state with four phases, is still not fully classified. The distinctive feature of the equilibrium case is large entropy of the ordered arrangements of $2\times 2$ square objects [17, 21-22]. \ \ \NI \UN{\bf 3.~Frozen States at Large Times} \ Let us consider first the case of the periodic (even-sized) two-dimensional square lattice. Due to diffusional relaxation the coverage $\theta$ reaches almost the fully crystalline value 1 for large times, $t \to \infty$. However, the final configuration on a finite-size lattice typically has frozen defects which are single-site and serve as points of origin of domain walls separating four different sublattice arrangements (``phases''). One such configuration is illustrated in Figure~1. The defects are locally ``gridlocked,'' and any state that contains all the empty area in such single-site isolated defects no longer evolves dynamically. The defect lines are either horizontal or vertical so that the resulting structure is essentially a random rectangular grid. There are no other types of defects here that can survive in the large-time limit, unlike other studies of the formation of two-dimensional frozen polycrystalline structures (by other growth mechanisms) available in the literature [23-24]. This freezing-in rectangular grid was also observed for a related equilibrium model [21] by slow cooling from a disordered configuration to zero temperature. The frozen network seems to depend profoundly on the boundary conditions; the rectangular grid is characteristic of periodic boundary conditions. Indeed, when a fixed boundary is used, where the particles are not allowed to occupy the sites outside the $L \times L$ square ($L$-even), the final configuration is always a regular pattern of $L\times L$ sites. In this case, it is obvious that whenever there are unoccupied defect sites, there must be also some unoccupied sites at the boundary. Through diffusion and deposition, the defect sites in the interior as well as the empty sites at the boundary are fully eliminated. The geometrical nature of the frozen grid pattern is illustrated by the following consideration. On a periodic two-dimensional lattice with even dimensions, the ``frozen'' network will have the geometry of the rectangular grid (Figure~1), i.e., a distribution of rectangular fully ordered domain shapes. Since each horizontal domain wall implies a shift of 1 lattice site, on an even periodic lattice the number of horizontal domain walls in each cross-section must be even. Similarly the number of vertical domain walls must be even. Thus the total number of domains, equal the number of single-site defects, is a product of two even numbers and must therefore be a multiple of 4. On the fixed-boundary lattice defined earlier, one simply cannot fit a rectangular array of domain walls with all vertices of coordination number 4. Thus, frozen states are not allowed due to purely geometrical constraints. Let $\rho (t)$ denote the density of the single-site defects. Numerically, we counted the number of unoccupied single sites fully surrounded by occupied sites, and divided by the total number of lattice sites, $L^2$. The large-time limiting values are plotted in Figure~2 vs.~the linear system size $L$. For system sizes $L>128$ it is difficult to reach the final limiting state. The data shown were obtained for the largest simulation times and they may be just upper bounds on the actual asymptotic values. The data indicate that the density decreases at least as fast as $1/L$. This also yields the deviation of the coverage at large time from the monocrystalline value 1. Thus, $1-\theta (\infty) \sim 1/L$, on a periodic lattice. The number of domains in the rectangular grid is equal to the number of vertices. If the domain size distribution were sharply peaked at some central value then the domain areas would saturate at $\sim L$. However, numerical evidence presented in Section~6 suggests that the domain linear size squared rather grows $\sim L^{1.6}$. This seems to suggest that the domain size, and possibly shape (i.e., rectangle size ratio), distributions are nontrivial and must be further investigated. Accurate domain statistics would require simulation of much larger lattices then those reported here. \ \ \NI \UN{\bf 4.~Time-Dependence of the Single-Site Defect Density} \ The single-site density $\rho (t)$ is plotted in Figure~3, on logarithmic scale, for several system sizes, $L$. It is interesting to note that $\rho (t)$ has a peak around $t=10$. For times $t<10$ the single-site density increases with time, and then decreases for large $t$. This is presumably due to the difference between dominant dynamical mechanisms for short and long times. In fact, results of this and later sections suggest that the dynamics has three distinct regimes. \NI\hang \UN{\sl Regime I.}\ \ For short times, the configuration is mainly build up by deposition. All types of structures, including the single-site defects, are produced. \NI\hang \UN{\sl Regime II.}\ \ At later times cluster coarsening occurs leading to ordering and formation of the frozen-grid defect structure. The defect structure in turn evolves from complicated to grid-like. \NI\hang \UN{\sl Regime III.}\ \ The latest stage of the dynamics consists of straightening up of defect lines and final freezing of the rectangular grid. This regime will be further commented on in the later sections. Finite-size effects show up already in Regime II: $\rho (t)$ saturates at $\sim 1/L$. The curves in Figure~3 then break off the main ``envelope'' which presumably corresponds to domain coarsening before the finite-size effects set in. This infinite-$L$ envelope in Regime II, i.e., for times $t>50$ in Figure~3, fits quite accurately the power law $$ \rho(t) \sim t^{-0.573 \pm 0.004}\;\; . \eqno(1) $$ \NI The precision of the power-law fit here is much higher than all other such fits reported in the present work. This presumably reflects absence of competing mechanisms in the Regime II. However, the exponent value for the growth of the linear domain size assuming one domain per one single-site defect, half the value in (1), $0.2865 \pm 0.002$, is smaller than the accepted value, 0.5, for the non-conserved dynamics in $2d$ [18-20]. Thus the simple domain-per-defect picture does not hold suggesting that Regime II corresponds not just to cluster coarsening but also to rearrangement of the empty area which consists not only of isolated single-site defects but includes more complicated, evolving structures. Thus, the power law in (1) cannot be simply explained by theories of cluster coarsening. The latter process will be further addressed in Section~6. \ \ \NI \UN{\bf 5.~Time-Dependence of the Coverage} \ The empty area fraction, $1-\theta$, is shown in Figure~4. Generally for large times we expect the empty area to be represented by terms with different time dependence: single-site, dimer vacancies, trimers, etc., $$ \theta(t) = 1 - \rho(t) - 2 \rho_{\rm dimer}(t) - \ldots \;\; . \eqno(2)$$ \NI Specifically, the eventual saturation of the different-$L$ curves suggested in Figure~4, is due to the fact that $\rho (t)$ remains small but finite (of order $1/L$) for large times. Consideration of the actual dynamical time steps achieved by writing a ``movie'' program to reproduce the consecutive configurations on the X-windows screen, has lead us to believe that the longest-surviving multiple-site empty area fragments are dimers. In the time Regime III, the grid structure has already been formed. However, the domain walls have kinks which are formed by dimer (two-site) empty-area defects. These can diffuse along the domain walls and ``interact'' with single-site defects while turning 90$^\circ$ at each such encounter. The kinks can also sometimes ``annihilate'' pairwise due to deposition when they come in contact in the appropriate configurations. A mapping to a reaction-diffusion system is suggested. However, here it will be more complicated than in $1d$ [13-15] where the ``diffusers'' were all identical and annihilated (with some probability) on pairwise encounters. If we speculate that the random grid is effectively one-dimensional and the reaction-diffusion system of dimer defects is otherwise similar to the $1d$ case, then we have the prediction $$ \rho_{\rm dimer}(t) \sim 1/ \sqrt{t} \;\; , \eqno(3) $$ \NI for large times, in the Regime III. Upon onset of saturation, the curves in Figure~4 become size-dependent. If we select the portions of the curves which follow the $L$-independent ``envelope,'' then we can fit the effective power-law, $$ 1 - \theta(t) \sim t^{-\alpha} \; \; . \eqno(4) $$ \NI However, least-square fits give exponent $\alpha$ values decreasing from 0.61 to 0.53, as $t$ increases. This deviation from the prediction (3) may be in part due to the use of 1 instead of the correct, $L$-dependent limiting value $\theta( \infty ) = 1 - \rho ( \infty ) $, and in part due to higher-order terms in (2). Indeed, for lattice sizes and times reached in our simulation the effective power-law fit here can be seen to largely cover Regime II rather than Regime III. \ \ \NI \UN{\bf 6.~Domain Size Measures} \ We considered two definitions for the linear domain size. The first is obtained via the average ``magnetization'' vector, ${\bf M}$, where each $2 \times 2$ object is labeled by a unit vector, directed up, down, left, right depending on which sublattice the object is in. The domain size is defined by $$ \ell_m = {4\over L } \left\langle {\bf M}^2 \right\rangle^{1/2} \;\; . \eqno(5) $$ \NI Here ${\bf M}$ is defined as the vector sum of the unit vectors of each of the deposited objects. The average $\langle \ldots \rangle$ is with respect to different Monte Carlo runs. Note that for a uniform single domain without defects, the domain size is $L$. The second definition is via the average square cluster size, $$\ell_c = {4\over L } \bigl\langle \sum_i c_i^2 \bigr\rangle^{1/2} \;\; , \eqno(6) $$ \NI where the clusters are defined as sets of squares on the same sublattice and continuously connected with each other; $c_i$ is the number of squares in the cluster $i$. Figure~5 shows the domain sizes, $\ell_c$, vs.~time, for various values of $L$. The results for $\ell_m$ (not shown) is similar but less accurate. By comparison between different sizes, we concluded that the data for $L=512$ and $t<2000$ should not show finite-size effect. Power-law least-squares fit $$ \ell_{m,c} \propto t^\beta\;\; \eqno(7)$$ \NI to the infinite-size result gives the exponent $\beta$ varying from 0.50 (for small $t$) to 0.36 (for large $t$) in different time intervals. It is therefore unlikely that the standard non-conserved-dynamics cluster growth exponent, $1 \over 2$ [12,18-20], can be accurately confirmed for this model without further much more extensive simulations. The domain size saturates for finite $L$. The dependence of the saturation value on the size $L$ is plotted in Figure~6, on logarithmic scale. These data are quite well fit by the power law, $$ \ell_{c,m}(t \to \infty) \sim L^{0.80\pm0.02} \;\; . \eqno(8)$$ Finally, let us stress that the results of this section were for periodic boundary conditions. Preliminary data indicate that the behavior of the cluster sizes, at least as far as their magnitudes go, is quite different for fixed boundary conditions. In summary we reported empirical observations and numerical exponent fits for the problem of lattice RSA with diffusional relaxation which is distinctive in that isolated defects are frozen in, leading to domain formation and strong dependence on boundary conditions. Unfortunately, both analytical understanding of such dynamical systems is very limited, and numerical results should be considered as preliminary. Future effort must be focussed on exploring other models but also on obtaining further high-quality numerical Monte Carlo results for the $2 \times 2$ model on the square lattice considered in this work. \ \ \NI \UN{\bf Acknowledgements} \ This work was supported in part by a Hong Kong Baptist College Faculty Research Grant (FRG/91-92/II-25) and by the DFG-Sonder\-forschungs\-bereich 262. P.N. wishes to thank the DFG for Heisenberg followship. \NP \centerline{\bf REFERENCES} {\frenchspacing \item{[1]} Review: M.C.~Bartelt and V.~Privman, Int. J.~Mod. Phys. B{\bf 5}, 2883 (1991). \item{[2]} Review: J.W.~Evans, Rev. Mod. Phys. (1993), in print. \item{[3]} J.~Feder and I.~Giaever, J.~Colloid Interface Sci. {\bf 78}, 144 (1980). \item{[4]} G.Y.~Onoda and E.G.~Liniger, Phys. Rev. A{\bf 33}, 715 (1986). \item{[5]} N.~Ryde, N.~Kallay and E.~Matijevi\'c, J.~Chem. Soc. Farad. Tr. {\bf 87}, 1377 (1991). \item{[6]} N.~Ryde, H.~Kihira and E.~Matijevi\'c, J.~Colloid Interface Sci. {\bf 151}, 421 (1992). \item{[7]} J.J.~Ramsden, preprint (1992). \item{[8]} See also J.J.~Ramsden, J.~Phys. Chem. {\bf 96}, 3388 (1992). \item{[9]} Y. Pomeau, J. Phys. A{\bf 13}, L193 (1980). \item{[10]} R.H. Swendsen, Phys. Rev. A{\bf 24}, 504 (1981). \item{[11]} V.~Privman, J.--S.~Wang and P.~Nielaba, Phys. Rev. B{\bf 43}, 3366 (1991). \item{[12]} J.--S.~Wang, P.~Nielaba and V.~Privman, Mod. Phys. Lett. B{\bf 7}, 189 (1993). \item{[13]} V.~Privman and P.~Nielaba, Europhys. Lett. {\bf 18}, 673 (1992). \item{[14]} P.~Nielaba and V.~Privman, Mod. Phys. Lett. B {\bf 6}, 533 (1992). \item{[15]} V.~Privman and M.~Barma, J.~Chem. Phys. {\bf 97}, 6714 (1992). \item{[16]} G. Tarjus, P. Schaaf and J. Talbot, J.~Chem. Phys. {\bf 93}, 8352 (1990). \item{[17]} L.K.~Runnels, in {\sl Phase Transitions and Critical Phenomena}, Vol.~2, p.~305, C.~Domb and M.S.~Green, eds. (Academic, London, 1972). \item{[18]} J.D.~Gunton, M.~San~Miguel, P.S.~Sahni, {\sl Phase Transitions and Critical Phenomena}, Vol.~8, p.~267, C.~Domb and J.L.~Lebowitz, eds. (Academic, London, 1983). \item{[19]} O.G.~Mouritsen, in {\sl Kinetics and Ordering and Growth at Surfaces}, p.~1, M.G. Lagally, ed. (Plenum, NY, 1990). \item{[20]} A.~Sadiq and K.~Binder, J.~Stat. Phys. {\bf 35}, 517 (1984). \item{[21]} K. Binder and D.P. Landau, Phys. Rev. B{\bf 21}, 1941 (1980). \item{[22]} W. Kinzel and M. Schick, Phys. Rev. B{\bf 24}, 324 (1981). \item{[23]} B.D. Lubachevsky and F.H. Stillinger, J. Stat. Phys. {\bf 60}, 561 (1990), and references therein. \item{[24]} See also B.D. Lubachevsky, F.H. Stillinger and E.N. Pinson, J. Stat. Phys. {\bf 64}, 501 (1991). } \NP \centerline{\bf FIGURE CAPTIONS} \ \noindent\hang{\bf Fig.~1.}\ \ A ``frozen'' configuration with four defect sites, on the $32 \times 32$ lattice. The $2\times 2$ deposited objects are shown as square outlines while the defects are shown as four ``holes'' half the linear size of the outlined objects. The periodic lattice was cut in such a way as to keep the $2\times 2$ objects whole. \ \noindent\hang{\bf Fig.~2.}\ \ Density of the isolated single-site defects at large times, plotted vs.~the linear system size $L$, on logarithmic scale. The sizes and times, $(L,\,t)$, were (8, 100), (16, 400), (32, 800), (64, $10^3$), (128, $10^4$), (256, $10^4$), (512, $10^5$). The data were averaged over several hundreds to few thousands of independent Monte Carlo runs. \ \noindent\hang{\bf Fig.~3.}\ \ The single-site density plotted on logarithmic scale as a function of time. The numbers indicate the system size $L$. The data were averaged over several hundreds to few thousands of independent Monte Carlo runs. \ \noindent\hang{\bf Fig.~4.}\ \ Empty area fraction, $1-\theta$, plotted vs.~time, $t$, on logarithmic scale. The system sizes were $L=2^n$, with $n$ from 3 to 9, from left to right, respectively. \ \noindent\hang{\bf Fig.~5.}\ \ Effective domain size $\ell_c$ plotted vs.~time $t$ on logarithmic scale, for system sizes $L$ indicated in the figure. (The noise in the larger-$L$ data and the break in the $L=64$ data are, respectively, due to low statistics and due to combining data from different-statistics runs.) \ \noindent\hang{\bf Fig.~6.}\ \ Domain size at saturation vs.~the system size $L$ on logarithmic scale. The solid circles are data for $\ell_c$, and open triangles are data for $\ell_m$. 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m 2632 1575 l 2642 1619 m 2632 1619 l 2642 1656 m 2632 1656 l 2642 1690 m 2632 1690 l 2642 1915 m 2632 1915 l 2642 2029 m 2632 2029 l stroke 528 419 m 548 419 l 528 1069 m 548 1069 l 528 1719 m 548 1719 l 2642 419 m 2622 419 l 2642 1069 m 2622 1069 l 2642 1719 m 2622 1719 l /Helvetica findfont 60 scalefont setfont stroke 490 419 m gsave 490 419 translate 0 rotate 0 -20 m (10-4) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-4) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 490 1069 m gsave 490 1069 translate 0 rotate 0 -20 m (10-3) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 490 1719 m gsave 490 1719 translate 0 rotate 0 -20 m (10-2) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont /Symbol findfont 87 scalefont setfont 324 1224 m gsave 324 1224 translate 90 rotate 0 0 m (r) CS (r) show grestore 1 setlinewidth /Symbol findfont 90 scalefont setfont /Helvetica findfont 90 scalefont setfont /Helvetica findfont 60 scalefont setfont newpath 2365 524 13 0 360 arc closepath fill stroke newpath 2078 867 13 0 360 arc closepath fill stroke newpath 1792 1070 13 0 360 arc closepath fill stroke newpath 1506 1324 13 0 360 arc closepath fill stroke newpath 1219 1537 13 0 360 arc closepath fill stroke newpath 933 1709 13 0 360 arc closepath fill stroke newpath 646 1748 13 0 360 arc closepath fill stroke /Helvetica findfont 30 scalefont setfont 300 50 moveto (FIG. 2 Wang et al) show showpage %%Trailer %%BoundingBox: 126 100 634 486 %%======================(Figure 3 begins here)=================== %!PostScript %%This is Figure 3, single-site density vs time for L=8, to 256 %%BoundingBox: (atend) %%Creator: Xmgr version 2.07 - PJ Turner OGI-ESE %%EndComments /m {moveto} bind def /l {lineto} bind def /RJ { stringwidth neg exch neg exch rmoveto } bind def /CS { stringwidth 2 div neg exch 2 div neg exch rmoveto } bind def /Helvetica findfont 15 scalefont setfont /rshow { gsave 90 rotate show grestore } bind def 139 317 m (8) rshow 157 421 m (16) rshow 242 478 m (32) rshow 343 603 m (64) rshow 439 559 m (128) rshow 451 629 m (256) rshow 0.25 0.25 scale 1 setlinecap 90 rotate 0 -2300 translate 0.000000 0.000000 0.000000 setrgbcolor 1 setlinewidth /Times-Italic findfont 60 scalefont setfont [] 0 setdash 3 setlinewidth 528 419 m 528 2029 l 2641 2029 l 2641 419 l 528 419 l stroke 1 setlinewidth [] 0 setdash 3 setlinewidth 740 419 m 740 429 l 864 419 m 864 429 l 952 419 m 952 429 l 1020 419 m 1020 429 l 1076 419 m 1076 429 l 1123 419 m 1123 429 l 1164 419 m 1164 429 l 1200 419 m 1200 429 l 1444 419 m 1444 429 l 1568 419 m 1568 429 l 1656 419 m 1656 429 l 1725 419 m 1725 429 l 1781 419 m 1781 429 l 1828 419 m 1828 429 l 1869 419 m 1869 429 l 1905 419 m 1905 429 l 2149 419 m 2149 429 l 2273 419 m 2273 429 l 2361 419 m 2361 429 l 2429 419 m 2429 429 l 2485 419 m 2485 429 l 2532 419 m 2532 429 l 2573 419 m 2573 429 l 2609 419 m 2609 429 l 740 2029 m 740 2019 l 864 2029 m 864 2019 l 952 2029 m 952 2019 l 1020 2029 m 1020 2019 l 1076 2029 m 1076 2019 l 1123 2029 m 1123 2019 l 1164 2029 m 1164 2019 l 1200 2029 m 1200 2019 l 1444 2029 m 1444 2019 l 1568 2029 m 1568 2019 l 1656 2029 m 1656 2019 l 1725 2029 m 1725 2019 l 1781 2029 m 1781 2019 l 1828 2029 m 1828 2019 l 1869 2029 m 1869 2019 l 1905 2029 m 1905 2019 l 2149 2029 m 2149 2019 l 2273 2029 m 2273 2019 l 2361 2029 m 2361 2019 l 2429 2029 m 2429 2019 l 2485 2029 m 2485 2019 l 2532 2029 m 2532 2019 l 2573 2029 m 2573 2019 l 2609 2029 m 2609 2019 l stroke 528 419 m 528 439 l 1232 419 m 1232 439 l 1937 419 m 1937 439 l 2641 419 m 2641 439 l 528 2029 m 528 2009 l 1232 2029 m 1232 2009 l 1937 2029 m 1937 2009 l 2641 2029 m 2641 2009 l /Times-Italic findfont 60 scalefont setfont /Helvetica findfont 60 scalefont setfont stroke 528 369 m gsave 528 369 translate 0 rotate 0 -20 m (101) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (1) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1232 369 m gsave 1232 369 translate 0 rotate 0 -20 m (102) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1937 369 m gsave 1937 369 translate 0 rotate 0 -20 m (103) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 2641 369 m gsave 2641 369 translate 0 rotate 0 -20 m (104) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (4) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont 1584 269 m gsave 1584 269 translate 0 rotate 0 0 m (t) CS (t) show grestore 528 792 m 538 792 l 528 1010 m 538 1010 l 528 1165 m 538 1165 l 528 1284 m 538 1284 l 528 1382 m 538 1382 l 528 1465 m 538 1465 l 528 1537 m 538 1537 l 528 1600 m 538 1600 l 528 2029 m 538 2029 l 2641 792 m 2631 792 l 2641 1010 m 2631 1010 l 2641 1165 m 2631 1165 l 2641 1284 m 2631 1284 l 2641 1382 m 2631 1382 l 2641 1465 m 2631 1465 l 2641 1537 m 2631 1537 l 2641 1600 m 2631 1600 l 2641 2029 m 2631 2029 l stroke 528 419 m 548 419 l 528 1657 m 548 1657 l 2641 419 m 2621 419 l 2641 1657 m 2621 1657 l /Helvetica findfont 60 scalefont setfont stroke 490 419 m gsave 490 419 translate 0 rotate 0 -20 m (10-3) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 490 1657 m gsave 490 1657 translate 0 rotate 0 -20 m (10-2) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont /Symbol findfont 87 scalefont setfont 324 1224 m gsave 324 1224 translate 90 rotate 0 0 m (r) CS (r) show grestore 1 setlinewidth /Symbol findfont 90 scalefont setfont /Helvetica findfont 90 scalefont setfont /Helvetica findfont 60 scalefont setfont 3 setlinewidth 459 1300 m 528 1394 m 671 1593 l 795 1679 l 883 1710 l 952 1715 l 1008 1714 l 1055 1706 l 1096 1697 l 1132 1681 l 1164 1668 l 1193 1653 l 1220 1639 l 1244 1625 l 1267 1614 l 1288 1599 l 1308 1586 l 1326 1572 l 1344 1560 l 1360 1545 l 1376 1534 l 1391 1522 l 1405 1510 l 1419 1497 l 1432 1486 l 1444 1475 l 1456 1465 l 1468 1454 l 1479 1444 l 1490 1436 l 1500 1427 l 1510 1417 l 1520 1408 l 1529 1398 l 1538 1390 l 1547 1381 l 1556 1374 l 1564 1365 l 1572 1356 l 1580 1349 l 1588 1341 l 1596 1335 l 1603 1330 l 1610 1321 l 1617 1314 l 1624 1306 l 1631 1300 l 1637 1294 l 1644 1284 l 1650 1281 l 1656 1274 l 1662 1268 l 1668 1263 l 1674 1256 l 1680 1250 l 1686 1246 l 1691 1241 l 1697 1237 l 1702 1232 l 1707 1225 l 1712 1219 l 1717 1213 l 1722 1209 l 1727 1204 l 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940 l 1993 939 l 1995 935 l 1997 933 l 1999 933 l 2001 929 l 2003 927 l 2005 924 l 2007 923 l 2009 921 l 2010 919 l 2012 915 l 2014 917 l 2016 911 l 2018 909 l 2020 908 l 2022 907 l 2024 905 l 2025 903 l 2027 900 l 2029 899 l 2031 900 l 2033 900 l 2035 900 l 2036 898 l 2038 894 l 2040 892 l 2042 892 l 2043 888 l 2045 888 l 2047 887 l 2048 881 l 2050 880 l 2052 880 l 2053 880 l 2055 877 l 2057 876 l 2058 873 l 2060 872 l 2062 871 l 2063 866 l 2065 863 l 2067 865 l 2068 863 l 2070 860 l 2071 860 l 2073 857 l 2074 856 l 2076 854 l 2078 857 l 2079 853 l 2081 849 l 2082 846 l 2084 845 l 2085 844 l 2087 841 l 2088 841 l 2090 838 l 2091 834 l 2093 835 l 2094 834 l 2096 833 l 2097 834 l 2099 830 l 2100 830 l 2101 831 l 2103 829 l 2104 825 l 2106 824 l 2107 823 l 2108 823 l 2110 824 l 2111 824 l 2113 822 l 2114 819 l 2115 817 l 2117 815 l 2118 816 l 2119 813 l 2121 811 l 2122 808 l 2123 809 l 2125 808 l 2126 806 l 2127 803 l 2129 802 l 2130 801 l 2131 798 l 2133 798 l 2134 798 l 2135 798 l 2136 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l 2331 906 l 2331 905 l 2332 906 l 2333 906 l 2334 906 l 2335 905 l 2336 906 l 2336 906 l 2337 906 l 2338 906 l 2339 906 l 2340 906 l 2341 906 l 2341 906 l 2342 906 l 2343 906 l 2344 906 l 2345 906 l 2345 906 l 2346 906 l 2347 906 l 2348 906 l 2349 906 l 2349 906 l 2350 906 l 2351 906 l 2352 906 l 2353 907 l 2353 906 l 2354 906 l 2355 906 l 2356 906 l 2356 906 l 2357 906 l 2358 906 l 2359 906 l 2360 906 l 2360 906 l 2361 906 l stroke 1 setlinewidth 3 setlinewidth 459 1302 m 528 1395 m 671 1592 l 795 1679 l 883 1709 l 952 1717 l 1008 1715 l 1055 1705 l 1096 1696 l 1132 1682 l 1164 1667 l 1193 1650 l 1220 1634 l 1244 1618 l 1267 1602 l 1288 1585 l 1308 1570 l 1326 1555 l 1344 1541 l 1360 1526 l 1376 1513 l 1391 1500 l 1405 1487 l 1419 1474 l 1432 1463 l 1444 1451 l 1456 1441 l 1468 1431 l 1479 1422 l 1490 1412 l 1500 1405 l 1510 1397 l 1520 1389 l 1529 1383 l 1538 1377 l 1547 1371 l 1556 1365 l 1564 1360 l 1572 1355 l 1580 1351 l 1588 1346 l 1596 1342 l 1603 1339 l 1610 1335 l 1617 1332 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l 843 1617 l 883 1629 l 920 1637 l 952 1645 l 981 1651 l 1008 1657 l 1032 1663 l 1055 1667 l 1076 1672 l 1096 1677 l 1114 1682 l 1132 1686 l 1148 1691 l 1164 1695 l 1179 1698 l 1193 1702 l 1207 1705 l 1220 1708 l 1232 1711 l stroke 1 setlinewidth /Helvetica findfont 30 scalefont setfont 300 50 moveto (FIG. 3 Wang et al) show showpage %%Trailer %%BoundingBox: 59 100 633 486 %%======================(Figure 4 begins here)=================== %!PostScript %%This is Figure 4. the 1-theta vs times for variable system size L %%BoundingBox: (atend) %%Creator: Xmgr version 2.07 - PJ Turner OGI-ESE %%EndComments /m {moveto} bind def /l {lineto} bind def /RJ { stringwidth neg exch neg exch rmoveto } bind def /CS { stringwidth 2 div neg exch 2 div neg exch rmoveto } bind def 0.25 0.25 scale 1 setlinecap 90 rotate 0 -2300 translate 0.000000 0.000000 0.000000 setrgbcolor 1 setlinewidth /Times-Italic findfont 60 scalefont setfont [] 0 setdash 3 setlinewidth 528 420 m 528 2029 l 2641 2029 l 2641 420 l 528 420 l stroke 1 setlinewidth [] 0 setdash 3 setlinewidth 740 420 m 740 430 l 864 420 m 864 430 l 952 420 m 952 430 l 1020 420 m 1020 430 l 1076 420 m 1076 430 l 1123 420 m 1123 430 l 1164 420 m 1164 430 l 1200 420 m 1200 430 l 1444 420 m 1444 430 l 1568 420 m 1568 430 l 1656 420 m 1656 430 l 1725 420 m 1725 430 l 1781 420 m 1781 430 l 1828 420 m 1828 430 l 1869 420 m 1869 430 l 1905 420 m 1905 430 l 2149 420 m 2149 430 l 2273 420 m 2273 430 l 2361 420 m 2361 430 l 2429 420 m 2429 430 l 2485 420 m 2485 430 l 2532 420 m 2532 430 l 2573 420 m 2573 430 l 2609 420 m 2609 430 l 740 2030 m 740 2020 l 864 2030 m 864 2020 l 952 2030 m 952 2020 l 1020 2030 m 1020 2020 l 1076 2030 m 1076 2020 l 1123 2030 m 1123 2020 l 1164 2030 m 1164 2020 l 1200 2030 m 1200 2020 l 1444 2030 m 1444 2020 l 1568 2030 m 1568 2020 l 1656 2030 m 1656 2020 l 1725 2030 m 1725 2020 l 1781 2030 m 1781 2020 l 1828 2030 m 1828 2020 l 1869 2030 m 1869 2020 l 1905 2030 m 1905 2020 l 2149 2030 m 2149 2020 l 2273 2030 m 2273 2020 l 2361 2030 m 2361 2020 l 2429 2030 m 2429 2020 l 2485 2030 m 2485 2020 l 2532 2030 m 2532 2020 l 2573 2030 m 2573 2020 l 2609 2030 m 2609 2020 l stroke 528 420 m 528 440 l 1232 420 m 1232 440 l 1937 420 m 1937 440 l 2641 420 m 2641 440 l 528 2030 m 528 2010 l 1232 2030 m 1232 2010 l 1937 2030 m 1937 2010 l 2641 2030 m 2641 2010 l /Times-Italic findfont 60 scalefont setfont /Helvetica findfont 60 scalefont setfont stroke 528 370 m gsave 528 370 translate 0 rotate 0 -20 m (101) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (1) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1232 370 m gsave 1232 370 translate 0 rotate 0 -20 m (102) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1937 370 m gsave 1937 370 translate 0 rotate 0 -20 m (103) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 2641 370 m gsave 2641 370 translate 0 rotate 0 -20 m (104) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (4) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont 1584 270 m gsave 1584 270 translate 0 rotate 0 0 m (t) CS (t) show grestore 528 615 m 538 615 l 528 730 m 538 730 l 528 811 m 538 811 l 528 874 m 538 874 l 528 925 m 538 925 l 528 969 m 538 969 l 528 1006 m 538 1006 l 528 1040 m 538 1040 l 528 1265 m 538 1265 l 528 1380 m 538 1380 l 528 1461 m 538 1461 l 528 1524 m 538 1524 l 528 1575 m 538 1575 l 528 1619 m 538 1619 l 528 1656 m 538 1656 l 528 1690 m 538 1690 l 528 1915 m 538 1915 l 528 2030 m 538 2030 l 2641 615 m 2631 615 l 2641 730 m 2631 730 l 2641 811 m 2631 811 l 2641 874 m 2631 874 l 2641 925 m 2631 925 l 2641 969 m 2631 969 l 2641 1006 m 2631 1006 l 2641 1040 m 2631 1040 l 2641 1265 m 2631 1265 l 2641 1380 m 2631 1380 l 2641 1461 m 2631 1461 l 2641 1524 m 2631 1524 l 2641 1575 m 2631 1575 l 2641 1619 m 2631 1619 l 2641 1656 m 2631 1656 l 2641 1690 m 2631 1690 l 2641 1915 m 2631 1915 l 2641 2030 m 2631 2030 l stroke 528 420 m 548 420 l 528 1069 m 548 1069 l 528 1719 m 548 1719 l 2641 420 m 2621 420 l 2641 1069 m 2621 1069 l 2641 1719 m 2621 1719 l /Helvetica findfont 60 scalefont setfont stroke 490 420 m gsave 490 420 translate 0 rotate 0 -20 m (10-3) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 490 1069 m gsave 490 1069 translate 0 rotate 0 -20 m (10-2) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 490 1719 m gsave 490 1719 translate 0 rotate 0 -20 m (10-1) RJ (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (-1) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont /Symbol findfont 87 scalefont setfont 324 1225 m gsave 324 1225 translate 90 rotate 0 0 m (1-q) CS (1-q) show grestore 1 setlinewidth /Symbol findfont 90 scalefont setfont /Helvetica findfont 90 scalefont setfont /Helvetica findfont 60 scalefont setfont 3 setlinewidth 528 2023 m 740 1928 l 864 1869 l 952 1826 l 1020 1792 l 1076 1763 l 1123 1738 l 1164 1715 l 1200 1696 l 1232 1678 l 1261 1661 l 1288 1646 l 1312 1632 l 1335 1619 l 1356 1606 l 1376 1595 l 1395 1584 l 1412 1574 l 1429 1564 l 1444 1555 l 1459 1546 l 1473 1538 l 1487 1529 l 1500 1522 l 1513 1514 l 1525 1507 l 1536 1500 l 1547 1494 l 1558 1487 l 1568 1481 l 1578 1475 l 1588 1470 l 1598 1464 l 1607 1459 l 1616 1454 l 1624 1449 l 1633 1444 l 1641 1439 l 1649 1435 l 1656 1430 l 1664 1426 l 1671 1421 l 1679 1417 l 1686 1413 l 1692 1409 l 1699 1406 l 1706 1402 l 1712 1398 l 1719 1395 l 1725 1391 l 1731 1388 l 1737 1384 l 1743 1381 l 1748 1378 l 1754 1375 l 1759 1371 l 1765 1368 l 1770 1365 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2496 998 l 2497 998 l 2497 998 l 2498 997 l 2498 997 l 2498 997 l 2499 996 l 2499 996 l 2500 996 l 2500 996 l 2500 995 l 2501 995 l 2501 995 l 2501 995 l 2502 995 l 2502 994 l 2503 994 l 2503 994 l 2503 993 l 2504 993 l 2504 993 l 2505 993 l 2505 992 l stroke 2505 992 m 2505 992 m 2505 992 l 2506 992 l 2506 991 l 2506 991 l 2507 991 l 2507 991 l 2508 990 l 2508 990 l 2508 990 l 2509 990 l 2509 990 l 2509 989 l 2510 989 l 2510 989 l 2511 988 l 2511 988 l 2511 988 l 2512 988 l 2512 987 l 2512 987 l 2513 987 l 2513 987 l 2514 986 l 2514 986 l 2514 986 l 2515 986 l 2515 985 l 2515 985 l 2516 985 l 2516 985 l 2517 984 l 2517 984 l 2517 984 l 2518 984 l 2518 983 l 2518 983 l 2519 983 l 2519 983 l 2519 982 l 2520 982 l 2520 982 l 2521 982 l 2521 981 l 2521 981 l 2522 981 l 2522 980 l 2522 980 l 2523 980 l 2523 980 l 2523 979 l 2524 979 l 2524 979 l 2525 978 l 2525 978 l 2525 978 l 2526 978 l 2526 977 l 2526 977 l 2527 977 l 2527 977 l 2527 976 l 2528 976 l 2528 976 l 2528 976 l 2529 976 l 2529 975 l 2530 975 l 2530 975 l 2530 975 l 2531 974 l 2531 974 l 2531 974 l 2532 974 l 2532 973 l 2532 973 l stroke 1 setlinewidth 3 setlinewidth 459 2053 m 528 2022 m 671 1959 l 795 1902 l 883 1860 l 952 1826 l 1008 1798 l 1055 1774 l 1096 1752 l 1132 1733 l 1164 1715 l 1193 1699 l 1220 1685 l 1244 1671 l 1267 1658 l 1288 1646 l 1308 1635 l 1326 1624 l 1344 1614 l 1360 1604 l 1376 1595 l 1391 1586 l 1405 1578 l 1419 1570 l 1432 1562 l 1444 1554 l 1456 1547 l 1468 1540 l 1479 1534 l 1490 1528 l 1500 1521 l 1510 1515 l 1520 1510 l 1529 1504 l 1538 1499 l 1547 1494 l 1556 1488 l 1564 1483 l 1572 1479 l 1580 1474 l 1588 1470 l 1596 1465 l 1603 1461 l 1610 1457 l 1617 1453 l 1624 1449 l 1631 1445 l 1637 1441 l 1644 1437 l 1650 1434 l 1656 1430 l 1662 1427 l 1668 1424 l 1674 1420 l 1680 1417 l 1686 1414 l 1691 1411 l 1697 1407 l 1702 1404 l 1707 1401 l 1712 1398 l 1717 1395 l 1722 1393 l 1727 1390 l 1732 1387 l 1737 1384 l 1741 1382 l 1746 1379 l 1751 1377 l 1755 1374 l 1759 1372 l 1764 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l 2003 1234 l 2005 1232 l 2007 1231 l 2009 1230 l 2010 1229 l 2012 1228 l 2014 1226 l 2016 1225 l 2018 1224 l 2020 1223 l 2022 1221 l 2024 1220 l 2025 1219 l 2027 1218 l 2029 1216 l 2031 1215 l 2033 1214 l 2035 1213 l 2036 1212 l 2038 1210 l 2040 1209 l 2042 1208 l 2043 1207 l 2045 1206 l 2047 1204 l 2048 1203 l 2050 1202 l 2052 1201 l 2053 1200 l 2055 1198 l 2057 1197 l 2058 1196 l 2060 1195 l 2062 1194 l 2063 1192 l 2065 1191 l 2067 1190 l 2068 1189 l 2070 1188 l 2071 1186 l 2073 1185 l 2074 1184 l 2076 1183 l 2078 1182 l 2079 1181 l 2081 1179 l 2082 1178 l 2084 1177 l 2085 1176 l 2087 1175 l 2088 1174 l 2090 1173 l 2091 1171 l 2093 1170 l 2094 1169 l 2096 1168 l 2097 1166 l 2099 1165 l 2100 1164 l 2101 1163 l 2103 1162 l 2104 1161 l 2106 1160 l 2107 1158 l 2108 1157 l 2110 1156 l 2111 1155 l 2113 1154 l 2114 1153 l 2115 1152 l 2117 1151 l 2118 1150 l 2119 1149 l 2121 1147 l 2122 1146 l 2123 1145 l 2125 1144 l 2126 1143 l 2127 1142 l 2129 1141 l 2130 1140 l 2131 1138 l 2133 1137 l 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1116 l 1647 1115 l 1650 1113 l 1653 1111 l 1656 1110 l stroke 1 setlinewidth 3 setlinewidth 247 2140 m 528 2015 m 583 1987 l 671 1935 l 740 1889 l 795 1847 l 843 1808 l 883 1770 l 920 1734 l 952 1699 l 981 1665 l 1008 1632 l 1032 1601 l 1055 1569 l 1076 1539 l 1096 1510 l 1114 1482 l 1132 1455 l 1148 1430 l 1164 1405 l 1179 1381 l 1193 1359 l 1207 1338 l 1220 1318 l 1232 1299 l stroke 1 setlinewidth /Helvetica findfont 30 scalefont setfont 300 50 moveto (FIG. 4 Wang et al) show showpage %%Trailer %%BoundingBox: 59 100 633 513 %%======================(Figure 5 begins here)=================== %!PostScript %%BoundingBox: (atend) %%Creator: Xmgr version 2.07 - PJ Turner OGI-ESE %%EndComments /m {moveto} bind def /l {lineto} bind def /RJ { stringwidth neg exch neg exch rmoveto } bind def /CS { stringwidth 2 div neg exch 2 div neg exch rmoveto } bind def /Helvetica findfont 15 scalefont setfont /rshow { gsave 90 rotate show grestore } bind def 335 486 m (8) rshow 287 509 m (16) rshow 236 556 m (32) rshow 187 613 m (64) rshow 123 622 m (128) rshow 160 509 m (512) rshow 0.25 0.25 scale 1 setlinecap 90 rotate 0 -2300 translate 0.000000 0.000000 0.000000 setrgbcolor 1 setlinewidth /Times-Italic findfont 60 scalefont setfont [] 0 setdash 3 setlinewidth 528 420 m 528 2030 l 2642 2030 l 2642 420 l 528 420 l stroke 1 setlinewidth [] 0 setdash 3 setlinewidth 687 420 m 687 430 l 780 420 m 780 430 l 846 420 m 846 430 l 897 420 m 897 430 l 939 420 m 939 430 l 974 420 m 974 430 l 1005 420 m 1005 430 l 1032 420 m 1032 430 l 1215 420 m 1215 430 l 1308 420 m 1308 430 l 1374 420 m 1374 430 l 1425 420 m 1425 430 l 1467 420 m 1467 430 l 1503 420 m 1503 430 l 1533 420 m 1533 430 l 1560 420 m 1560 430 l 1744 420 m 1744 430 l 1837 420 m 1837 430 l 1903 420 m 1903 430 l 1954 420 m 1954 430 l 1996 420 m 1996 430 l 2031 420 m 2031 430 l 2062 420 m 2062 430 l 2089 420 m 2089 430 l 2272 420 m 2272 430 l 2365 420 m 2365 430 l 2431 420 m 2431 430 l 2482 420 m 2482 430 l 2524 420 m 2524 430 l 2560 420 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2113 2030 m 2113 2010 l 2642 2030 m 2642 2010 l /Times-Italic findfont 60 scalefont setfont /Helvetica findfont 60 scalefont setfont stroke 528 370 m gsave 528 370 translate 0 rotate 0 -20 m (100) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (0) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1056 370 m gsave 1056 370 translate 0 rotate 0 -20 m (101) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (1) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 1585 370 m gsave 1585 370 translate 0 rotate 0 -20 m (102) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (2) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 2113 370 m gsave 2113 370 translate 0 rotate 0 -20 m (103) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (3) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore 2642 370 m gsave 2642 370 translate 0 rotate 0 -20 m (104) CS (10) show /Helvetica findfont 36 scalefont setfont 0 36 rmoveto (4) show /Helvetica findfont 60 scalefont setfont 0 -36 rmoveto () show grestore /Helvetica findfont 87 scalefont setfont 1585 270 m gsave 1585 270 translate 0 rotate 0 0 m (t) CS (t) show grestore 528 662 m 538 662 l 528 804 m 538 804 l 528 904 m 538 904 l 528 982 m 538 982 l 528 1046 m 538 1046 l 528 1100 m 538 1100 l 528 1146 m 538 1146 l 528 1188 m 538 1188 l 528 1467 m 538 1467 l 528 1609 m 538 1609 l 528 1709 m 538 1709 l 528 1787 m 538 1787 l 528 1851 m 538 1851 l 528 1905 m 538 1905 l 528 1951 m 538 1951 l 528 1993 m 538 1993 l 2642 662 m 2632 662 l 2642 804 m 2632 804 l 2642 904 m 2632 904 l 2642 982 m 2632 982 l 2642 1046 m 2632 1046 l 2642 1100 m 2632 1100 l 2642 1146 m 2632 1146 l 2642 1188 m 2632 1188 l 2642 1467 m 2632 1467 l 2642 1609 m 2632 1609 l 2642 1709 m 2632 1709 l 2642 1787 m 2632 1787 l 2642 1851 m 2632 1851 l 2642 1905 m 2632 1905 l 2642 1951 m 2632 1951 l 2642 1993 m 2632 1993 l stroke 528 420 m 548 420 l 528 1225 m 548 1225 l 528 2030 m 548 2030 l 2642 420 m 2622 420 l 2642 1225 m 2622 1225 l 2642 2030 m 2622 2030 l /Helvetica findfont 60 scalefont setfont stroke 490 420 m gsave 490 420 translate 0 rotate 0 -20 m (1) RJ (1) show grestore 490 1225 m gsave 490 1225 translate 0 rotate 0 -20 m (10) RJ (10) show grestore 490 2030 m gsave 490 2030 translate 0 rotate 0 -20 m (100) RJ (100) show grestore /Helvetica findfont 87 scalefont setfont /Times-Italic findfont 87 scalefont setfont 341 1225 m gsave 341 1225 translate 90 rotate 0 0 m (lc) CS (l) show /Times-Roman findfont 52 scalefont setfont 0 -26 rmoveto (c) show grestore 1 setlinewidth /Times-Roman findfont 90 scalefont setfont /Helvetica findfont 90 scalefont setfont /Helvetica findfont 60 scalefont setfont 3 setlinewidth 1056 854 m 1215 930 l 1308 967 l 1374 988 l 1425 1001 l 1467 1009 l 1503 1015 l 1533 1019 l 1560 1021 l 1585 1023 l 1606 1024 l 1626 1025 l 1645 1026 l 1662 1026 l 1678 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l 2195 1411 l 2197 1411 l 2198 1411 l 2200 1411 l 2201 1411 l 2203 1411 l 2205 1411 l 2206 1411 l 2208 1411 l 2209 1411 l 2211 1411 l 2212 1411 l 2214 1411 l 2215 1411 l 2217 1411 l 2218 1411 l 2219 1411 l 2221 1411 l 2222 1411 l 2224 1411 l 2225 1411 l 2227 1411 l 2228 1411 l 2229 1411 l 2231 1411 l 2232 1411 l 2233 1411 l 2235 1411 l 2236 1411 l 2237 1411 l 2239 1411 l 2240 1411 l 2241 1411 l 2243 1411 l 2244 1411 l 2245 1411 l 2247 1411 l 2248 1411 l 2249 1411 l 2250 1411 l 2252 1411 l 2253 1411 l 2254 1411 l 2255 1411 l 2257 1411 l 2258 1411 l 2259 1411 l 2260 1411 l 2262 1411 l 2263 1411 l 2264 1411 l 2265 1411 l 2266 1411 l 2267 1411 l 2269 1411 l 2270 1411 l 2271 1411 l 2272 1411 l stroke 1 setlinewidth 3 setlinewidth 1056 896 m 1215 1010 l 1308 1070 l 1374 1116 l 1425 1153 l 1467 1181 l 1503 1206 l 1533 1224 l 1560 1244 l 1585 1258 l 1606 1277 l 1626 1286 l 1645 1304 l 1662 1312 l 1678 1324 l 1692 1336 l 1706 1344 l 1719 1353 l 1732 1361 l 1744 1372 l 1755 1378 l 1765 1389 l 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