You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
core - softened @xmath0 potentials have been attracting attention due to their connections with the anomalous behavior of liquid systems including water . these potentials , u(r ) , exhibit a repulsive core with a softening region limited by @xmath1 where @xmath2 with @xmath3  @xcite .
despite their simplicity , these models originate from the desire of constructing a simple two - body isotropic potential capable of describing the complicated features of systems interacting via anisotropic potentials  @xcite .
this procedure generates models that are analytically tractable and computationally less expensive than the atomistic models . moreover
, they are lead to conclusions that are more universal and are related to families of atomistic systems  @xcite .
one of the features that has been successfully described by many of these models is the density anomaly . for water
the specific volume at ambient pressure starts to increase when cooled below @xmath4 .
the anomalous behavior of water was first suggested 300 years ago  @xcite and was confirmed by a number of experiments  @xcite . besides , between @xmath5 mpa and @xmath6 mpa water also exhibits an anomalous increase of compressibility  @xcite and , at atmospheric pressure , an increase of isobaric heat capacity upon cooling  @xcite . for the case of water
the density anomaly is attributed to the presence of hydrogen bonds between neighbor molecules .
as the temperature increases the bonds break and the density increases .
however , other systems such as te , @xcite ga , bi ,  @xcite s ,  @xcite , ge@xmath7te@xmath8 ,  @xcite , silica ,  @xcite silicon  @xcite and bef@xmath9 ,  @xcite show the same density anomaly without presenting hydrogen bonds what suggests that the mechanism for the presence of density anomaly might be more universal .
in compass with the presence of the density anomaly in water a few years ago it was suggested that there are two liquid phases , a low density liquid ( ldl ) and a high density liquid ( hdl )  @xcite .
the critical point ending this transition , found only in computer simulations is located at the supercooled region beyond the line of homogeneous nucleation and thus can not be experimentally measured .
even with this limitation , this hypothesis has been supported by indirect experimental results  @xcite .
the presence of two liquid phase and of second critical point is also observed in certain @xmath10 potentials  @xcite .    which are the conditions for a cs potential to exhibit density anomaly and two liquid phases ?
a definitive answer to this question is still missing .
there are , however , a few clues .
if a cs potential has discontinuous forces it presents two liquid phases but no density anomaly  @xcite is observed .
however , once the cs potential is modified to have continuous forces , the anomalies appear  @xcite .    recently it has been proposed that a cs potential exhibits density anomaly if the two length scales identified with the softened region would be accessible  @xcite what can be understood as follows . the radial distribution , @xmath11 of a cs potential has peaks at @xmath12 and @xmath13 where @xmath14 and @xmath15 are the two length scales of the cs potential  @xcite . if @xmath16 the model is introduced and the simulation details are presented . in sec .
[ sec : results ] the pressure - temperature phase diagram is presented together with the behavior of the radial distribution function with density and temperature .
conclusions are presented in sec .
[ sec : conclusions ] .
our system consists of @xmath17 identical particles interacting through a continuous pair potential obtained by the addition of @xmath18 different fermi - dirac distributions  @xcite , @xmath19 the resulting expression describes a family of pair interaction potentials discriminated by different choices of the parameters @xmath20 .
appropriated choices of the parameters allow us to obtain potentials that go from a smooth two length scales potential to a sharp , almost discontinuous , square potential  @xcite .    in the table  [ table : ref ]
nine different sets of parameters are shown , organized in three families named , @xmath21 , @xmath22 , and @xmath23 .
as shown in figure  [ fig : potential ] , for each family a specific characteristic of pair interaction potential is tuned .
then it is possible to test the effect of changing the two length scales in the pressure temperature phase diagram .    in the potentials
@xmath21 the slope between the two length scales is varied .
then it is possible to check if the slope between the two length scales controls the location in the pressure - temperature phase diagram of the density anomalous region as suggested by yan et al .
@xcite .    in the case of the potentials
@xmath22 , the attractive length becomes broader . consequently using this potential we test if increasing the range of the attraction leads to a decrease in the critical pressure as proposed by skibinsky et al .
@xcite .    in the case of the potentials
@xmath23 , the repulsive length scale becomes broader .
therefore this family of potentials is appropriated to observe if the enlargement of the repulsive length scale leads to a decrease in the liquid - liquid critical pressure and to an increase in the liquid - liquid critical temperature as suggested by skibinsky et al .
in addition to verify the assumptions of yan et al .
@xcite and of skibinsky et al .
@xcite related to criticality , these three families of potentials are the perfect scenario to check our hypothesis that the density anomaly region in the pressure - temperature phase diagram is delimited by properties of the radial distribution function at the two length scales .            .parameters for potentials @xmath21 , @xmath22 and @xmath23 in reduced units of @xmath24 and @xmath25 . [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ]     the figs .
[ fig : grcros ] show the value of the radial distribution function at the closest , @xmath12 ( dashed lines ) , and at the furthest scale , @xmath13 ( solid lines ) , as a function of the reduced density , @xmath26 . for the closest scale @xmath12
is monotonic with density while the value for the @xmath13 for a fixed temperature increases with the density for densities below the @xmath27 and decreases for densities above this threshold .
this behavior , also shown in the fig .
[ fig : gr ] , corroborates the condition stated in the eq .
[ eq : condition ] and supports the idea that particles move from one scale to the other by compression at @xmath28  @xcite .    besides to the move of particles from the attractive scale to the repulsive scale for @xmath29 as the pressure ( density ) is increased , particles also move from one scale to the other due to the increase of temperature  @xcite for @xmath27 . at constant density , @xmath27 ,
the radial distribution function of the attractive scale , @xmath13 , decreases with the increase of the temperature while @xmath12 increases with the increase of temperature , indicating that particles move from one scale to the other due to thermal effects . at the density @xmath30 , the value of @xmath12 is independent of the temperature .
potential for different temperatures for different pressures.,width=302 ]    what is the meaning of the density @xmath31 in which @xmath32 is independent of temperature ? as it was pointed in the previous paragraph , for @xmath27 particles move from the furthest scale , @xmath33 , to the closest scale , @xmath14 , using thermal energy as the temperature is increased . in this case
@xmath12 increases with temperature . for @xmath29 particles
move from @xmath33 to @xmath14 , using the increase of pressure pressure ( or density ) as illustrated by the eq .
[ eq : condition ] . from statistical point of view , the two mechanisms governing the behavior for @xmath29 and @xmath27 are quite different .
while increasing temperature affects particles individually , increasing the density or the pressure affects the particles as clusters or networks .
then , as the potential becomes more soft , the threshold density @xmath30 beyond which the particles move form one scale to the other by compression should decrease as observed in fig .
[ fig : grcros ] .
therefore @xmath30 is the threshold between these two mechanisms present in systems that have density anomaly .
in addition to these low density limit , the density anomalous systems also have a high density threshold , @xmath34 .
[ fig : grcros ] illustrates as a solid thick line the temperatures and densities , @xmath34 , in which @xmath35 .
since @xmath11 is related with the number of particles at distance @xmath36 , for @xmath37 more particles are in the attractive scale , @xmath33 , while for @xmath38 more particles are at the repulsive scale @xmath14 .
therefore , the thick solid line is a boundary between the high density liquid and the low density liquid .
analysis of the stability indicates that no real phase transition is observed across this line .    in order to understand what what happens in the region of the pressure - temperature phase diagram of the @xmath34 , the behavior of the specific heat in this region was analyzed .
[ fig : cp ] shows the curves of isobaric specific heat , for different pressures as a function of the temperature for the potential @xmath39 .
the peak of @xmath40 for each one of the potentials analyzed in this manuscript coincide with the region @xmath34 where @xmath35 .
this result indicates that the structure in the tmd region already build the liquid arrangements required for the liquid - liquid phase separation .
in this paper we have studied three families of core - softened potentials that exhibit two length scales , one repulsive , @xmath14 , and another attractive , @xmath33 .
we had observed that the region in the pressure - temperature phase diagram occupied by the tmd is quite sensitive to the slope between the two length scales . as the slope increases the region decreases .
we also found that the region in the pressure - temperature phase diagram where the density , diffusion and structural anomalous behavior is observed shifts to lower pressures and shrinks the attractive scales or the repulsive scales become wider .
our results suggests the competition between two length scales are the relevant mechanism for the existence of the tmd .    in an attempt to confirm this assertion we showed in this family of potentials that the condition @xmath41 seems to be associated with the presence of anomalous behavior .
in addition we also observed that the peaks of the radial distribution function at each length scales exhibit very distinct behavior with density and temperature suggesting two complementary mechanisms for the competition between the two scales .    at low densities ,
@xmath27 particles move from @xmath33 to @xmath14 with the increase of temperature , using thermal energy . for densities above
@xmath30 the increase of @xmath12 is associated with the increase in the pressure ( density ) . in this interval of densities at a certain density and temperature the radial distribution function at the first length scale equals the value at the second scale , namely @xmath35 .
this point can be identified with the widom line .
the relation between the radial distribution function and the widom line , believed to be the onset of the liquid - liquid phase transition give the support to the idea that the widom line separates two structural distinct regions that are also separated by a fragile - strong transition  @xcite .
we expect that his result will not only shade some light in the definition of what is the shape an effective core - softened would have in order to held anomalies but also would serve to reinforce the ideas of linking dynamic transitions and thermodynamic properties .
we thank for financial support the brazilian science agencies cnpq and capes . this work is partially supported by cnpq , inct - fcx .
three core - softened families of potentials are checked for the presence of density and diffusion anomalies . 
 these potentials exhibit a repulsive core with a softening region and at larger distances an attractive well . 
 we found that the region in the pressure - temperature phase diagram in which the anomalies are present increases if the slope between the core - softened scale and the attractive part of the potential decreases . 
 the anomalous region also increases if the range of the core - softened or of the attractive part of the potential decreases . 
 we also show that the presence of the density anomaly is consistent with the non monotonic changes of the radial distribution function at each one of the two scales when temperature and density are varied . 
 then , using this anomalous behavior of the structure we show that the pressures and the temperatures in which the radial distribution functions of the two length scales are equal are identified with the widom line .