optimal stability of binary granular mixtures

when mixtures form steeper slopes than either of its components

Several techniques have been employed to create a steeper pile out of a granular material. The most intuitive idea is to wet a granular medium to make it form a steeper pile.

Imagine experimenting with sand, as you may have done in the beach in the previous summer months. When very little amount of water is used to wet a pile of sand, the pile is still dry, and no significant increase in stability is observed. Add a little more water and the pile significantly becomes steeper; you can now form walls and towers of your sand castle. Upon reaching this point, you don't add more water to the pile; when more water is added, its behavior dominates and the pile is washed away.

In an experiment recently published in the journal Physica A, a team of scientists from the Complex Systems Group of the Instrumentation Physics Laboratory, National Institute of Physics was able to find an analog to such phenomenon of granular material stability; instead of using water, they used another granular medium, but this time of smaller grain sizes than the one in consideration [1]. The team is headed by Christopher Monterola, a pioneer in granular materials research in the country.

Experimental design

A plexi-glass box container with a motor-controlled opening wall carries the granular medium. The medium is mixed well, and upon opening the wall, some of the granular mixtures fall off to the edge. The resulting pile is stable and the angle of its inclination with respect to the floor of the container is taken as a quantitative measure of its stability.

The experimental setup. Click on image for larger view.

The procedure is done multiple times for different granular mixture types and different concentrations of the smaller particle. It was found out that the speed of opening the container does not affect the result much, so it was not included in the parameters under consideration.

The experiment revealed that steepest pile is formed also under optimal conditions: (1) The size difference of the materials is significantly large; (2) The larger grain must occupy about 50-70% of the available volume, and the smaller grain the remaining 30-50%. When these conditions are met, the pile is most stable because the smaller grains fill in the voids between larger grains, supporting its weight and avoiding more slippage, resulting in a pile with a higher angle of inclination.

Some configurations even show vertical slopes, perfect 90-degree regions near the top of the pile. This is not attained for granular-water mixtures, because water, as a liquid, cannot support weight.

Cellular automata (CA) model

The experimental results are further complemented by a lattice model. A 128 by 128 square grid is used as a 2D representation of the granular medium inside the container. By employing a probabilistic slipping rule and a condition for stopping the update, the model resulted in slopes that are similar to the ones observed experimentally.

Even more important is the fact that the CA model captured the vertical slope regions, also near the top of the heap. This is an important advantage of CA over continuum models, because continuum models require infinite coefficients of friction to achieve a 90-degree inclination, which is not realistic.

Implications to large-scale stability

Water content is the primary concern in assessing landslide risk zones such as cliffs and mountain slopes. The study hints to the possibility that the material sizes and their relative concentrations in the medium may be a crucial factor in determining stability of the slopes in these hazard-prone areas.

The group has recently provided evidence that small scale models have similar statistical signatures as empirical landslide surveys [2, see highlight]. The researchers hope that scaled-down approach, such as studies of these kind, could prove useful for studying the complex dynamics of landslide hazards.

1. R.Batac, M.Pastor, M. Arciaga, J. Bantang and C. Monterola, Kinks, logarithmic tails, and super-stability in bi-disperse granular media, Physica A 388, 3072-3082 (2009).
2. D. Juanico, A. Longjas, R. Batac and C. Monterola, Avalanche statistics of driven granular slides in a miniature mound, Geophys. Res. Lett., 35, L19403, doi:10.1029/2008GL035567, 2008.
   

can humans generate a purely random number sequence?

nope, individually; but a minimum of seven individuals can

Central to the study of psychophysics is the idea of numbers by individuals. While individuals have an inherent sense of number (which starts with the natural numbers, and base 10 by the number of fingers), certain ideas about numbers and number arrangements have only been acquired through education.

An example of such is the idea of random numbers. One encounters such sequences in statistical mechanics, in a simple model called the random walk, and the very idea is used to derive the profound principle of central limit theorem. But of the many possible distributions that are classified as "random" (uniform, Poisson, Gaussian), what exactly does the mind imagine it to be? The biases and the "misconceptions" of the mind when it comes to the idea of random number generation (RNG) is discussed in various papers, and one of the recent investigations have been conducted by a team of IPL Complex Systems Researchers composed of I. Crisologo, A. Longjas, E. Legara and C. Monterola. Their results are published in Pisika, the journal of the Philippine Society of Physics [1].

Not really random

The team studied the number combinations generated by human samples under three different conditions: that without a guide and those with guides printed on a flashboard: one board is unbiased (all numbers appear at equal frequencies) and the other is biased to a particular number (the number 2 appears more often).

In judging whether the generated sequence is random or not, the team used the fact that in a purely random sequence, the probability of finding a number followed by another is uniform or equally probable. For example, a "1" to be followed by a "2" is equally likely as it is being followed by a "3" or a "4" or any other number. Note that this does not exclude the possibility of finding a number followed by the same number: "1" followed by "9" is as likely as "1" followed by "1".

This the human mind does not seem to realize.

The research found out that humans generate a series with preference for different number series and bias against repetition of similar numbers. This behavior seems universal for all people involved and for all numbers studied.

Randomize

Appending the series of non-random sequences generated by individuals obviously will not correct the problem; i.e. the resulting sequence will still fail the randomness test. The researchers instead try to stitch the series: given N number of generated sequences of numbers {x}, they formed a stitched sequence of {X} where the first component is from the first series, the second component is from the second series, and so on.

This time, they find that the resulting sequence is random, based on the same criterion used for the appended sequence. The probability of finding all number series (this number followed by this number) are roughly the same.

Biasing the biased?

Guiding the person generating the series has its effects, the study notes. When the board shown the participants are biased to a certain number, that number not only appears more often in the resulting sequence, the probability of it appearing in series (i.e. it appears immediately after the same number) is significantly higher.

This result is counter-intuitive. Biasing, in effect, will drive the sequence to be more random.

Psychophysic(ist)s

The group investigates psychophysical phenomena, defined as the quantitative study of the way the mind perceives things.

Crisologo, the first author, is the youngest of the group, an undergraduate student of the University of the Philippines. The other members are faculty members of the National Institute of Physics of the same University.

1. I. Crisologo, A. Longjas, E. Legara and C. Monterola (2008). A procedure for generating a random number sequence using at least seven individuals. Pisika 2(1).

the complex classroom

seating arrangement, student homogeneity and student interaction affect how students learn

Classroom dynamics is not as simple as it may seem. The transfer of knowledge from teacher to students is intimately connected with the students' individual learning capabilities and prevailing classroom conditions. Effective educators know how to adjust the teaching strategies to account for these factors.

It has been shown that peer instruction can enhance learning rates for students in a class. Interaction between students provides a venue for healthy exchange of ideas without the imposing presence of the teacher. Dr. Eric Mazur, a Physics Professor at Harvard University realized this as he developed (in 1990) the Peer Instruction method of teaching, now adopted by successful educators around the world. The method is even more effective for handling large classes [1].

In the Philippine setting, classrooms are usually filled to the roof, especially in rural communities where there is shortage of teachers and teaching facilities. Moreover, students are usually grouped into sections based on their performance in the previous year: the brightest students are usually placed on a premier “star” section (section 1) and the rest are placed in sections of increasing numbers yet decreasing mean rating, and correspondingly, decreasing level of attention and concentration in terms of teaching and resources. These factors contribute to the continuing problem of primary and secondary education in the country. Peer instruction may prove to be a solution to these woes, but how effective really is it in the context of the real classroom, where students are grouped based on rank and seating is random?

The goal of the study conducted by Dr. C. Monterola, R. M. Roxas and S.L. Carreon-Monterola is to answer that question. In their paper published in the journal Complexity titled “Characterizing the Effect of Seating Arrangement on Classroom Learning Using Neural Networks,” they present results of actual classroom experiments coupled with neural network predictions [2].

Optimal seating arrangement

The perceived status of each student can be evaluated by the teacher either by grades in a previous course or by a pre-test, a short examination after a lecture and prior to student interactions. The scores of these tests may reveal who among the students remembered and understood the topics as discussed by the teacher. Of course, those who fared better are expected to play important roles in the peer instruction to follow – they will be the source of correct information to teach their other classmates.

The researchers tried to check if the spatial distribution of these students in class (i.e., where these brightest students are located in the classroom) will have a significant effect on the effectiveness of the peer instruction procedure. They measured the average increase in scores between the pre- and post-student interaction quizzes for different seating schemes: the brightest students are placed (1) randomly; (2) in the four corners; (3) in middle of the room; and (4) in an inner four corners.

Comparing the results for the following arrangements, they realized that marked improvement in class score is achieved when students are arranged such that the highest scorers are placed toward the outer four corners of the classroom. It is in this configuration that most low aptitude students get to interact with the high aptitude ones. In contrast, the paper describes that the “S[eating] A[rrangement] with high P[erceived] A[ptitude] L[evel] students concentrated at the center (less interaction opportunity for low PAL) has the lowest average” score gain. Neural network predictions generally agree with these experimental results.

The paper thus adds an important result to the Peer Instruction method of Mazur: the method will be more effective when applied to an optimal student arrangement that maximizes efficient transfer of information.

Groupings

There seems to be a basis for grouping students into sections of the same capabilities.

As for students with high aptitude levels, the paper straightforwardly says that “S[tudent] I[nteraction] O[pportunities] is deemed ineffective,” in the sense that bright students do not benefit that much. Whether it is because they already have high grades in the first place – or they are just stubborn – the paper doesn’t say.

On the other hand, students with low aptitude levels benefit more upon interaction with other students of comparable aptitude levels, the paper discusses. A significant increase in score gain is obtained after peer interaction between students of comparably lower aptitudes.

With this, it can be seen that the existing structure found in Philippine high schools can be considered to be optimized and thus may be utilized to further instruction and learning. That is, students from “lower” sections can be made to be competitive, by inclusion of peer instruction and student interaction in their curriculum.

Education research

Two of the authors form the education research subgroup of the Complex Systems Group, and their co-author is an educator herself from the College of Education in the same University.

Before being an Instructor in UP Diliman, R.M. Roxas served as a teacher in a university in her home province of Mindoro. Coming from a family of educators, this research is especially close to her heart.

C.P. Monterola and S.C. Monterola are a husband and wife team, both of whom are professors of the University. The former teaches Physics at the NIP and heads the Complex Systems Group, while the latter is considered to be one of the finest professors in the UP Integrated School, where she has handled the high school physics courses.■

1. E. Mazur. Peer Instruction: A User's Manual (Prentice Hall, 1997).
2. C. Monterola, R. Roxas, and S.L. Carreon-Monterola (2008). Characterizing the Effect of Seating Arrangement on Classroom Learning Using Neural Networks, Complexity (In press, doi:10.1002/cplx.20237).

tearing, reinforcement and damage accumulation

Computer model reveals effective reinforcement strategies for fabric


Clothes are primarily designed to shield us from extreme environments. But we rarely see a knight's armor in boutiques - if we can find one at all. There is clearly a trade-off between rigidity and comfort in garments design and in our own personal choice of outfit - clothes can never be too tight and stiff lest it should compromise user's comfort. Striking a balance between these two takes its toll on fabric, the main clothing material.

Softer, lighter fabric, say satin, will definitely tear faster when subjected to shearing forces compared to tougher ones, like jeans. The more one goes to the comfort end of the spectrum, the more this becomes true, highlighting the need for structural reinforcement procedures that prolong the lifetime of clothing without sacrificing comfort.

This is perhaps the motivation behind the research endeavor conducted by George Allan P. Esleta and Christopher P. Monterola [Complex Systems Researchers]. Their results, published in the journal Computer Physics Communications [1], prove useful in two aspects: (1) from a computational point of view, it provides an elegant model of tearing and cracking; and (2) it has a practical aspect to it, particularly its direct application to fabric.

Physical model

Stress propagation across a square grid network of interconnected springs is simply no trivial matter (at least for the introductory physics student) albeit the simplicity and linearity of Hooke's law: the force F on a spring is proportional to the amount of displacement x it has elongated relative to its unstretched length, F = -kx, with the spring constant k measuring the stiffness of the spring. For a network of springs, one has to consider a set of different stiffness values k. And as real springs have limitations as to the extent up to which they can be stretched, a model of such network must also incorporate a set of breaking lengths xmax, proportional to the spring constants.

Such model, while rather computationally challenging, is best for modeling fabric: since springs have k values, the interconnected springs naturally incorporates stiffness found in real fabric. The breaking lengths xmax, on the other hand, is a relative measure of stability. In a way, the researchers found a way to computationally model the trade-off discussed earlier. Think of satin, as previously described, as having low k translating into its being comfortable, while correspondingly having low xmax value resulting into its being easily torn apart. In the same manner, jeans will be modeled as having a high k for its being stiff and high xmax for its being durable.

Esleta, the main proponent of the paper, solved the problem numerically, using different force profiles along the sides of the fabric and counting for the number of spring breakings (i.e. fabric tearings). Upon knowing the critical locations where the network is expected to tear apart, reinforcement strategies can be developed, stiffening springs on a particular region subject to a given spatial distribution.

Strategies: Random vs. targeted vs. distributed

Randomly choosing springs to strengthen do not resolve the problem. Of course, targeted reinforcement (i.e. finding the site to collapse and strengthening it) is best, but it is tedious and nearly impractical in reality. For fabric, this means actual testing where actual points on the weave are weakest, an impossible job for a yard of fabric, much more a skirt or gown.

The remedy is still to have reinforcement distributed over an area. Of the distributions tested, the centered Gaussian area distribution of reinforcement proved efficient, followed by the doughnut.

But why not uniform distribution? Again, in the context of fabric, this means neglecting the balance and tipping the scales to the strength side at the expense of comfort, a scenario not really advantageous for the user.

What doesn't kill you will make you stronger?

In addition to these published results, the group presented a conference paper on the effect of accumulated stress on the system [2].

The effect of accumulated stress on the system is described by an empirical law attributed to Basquin: the plot of the lifetime of the material versus the applied force obey's a power-law relation with a negative exponent roughly equal to 2.

Esleta and Monterola’s result seem to support the dictum advocated by these earlier authors: What doesn’t kill you will make you weaker. Yes, they are not as optimistic as Nietzsche, for whom the words in the title of this section are credited.

Not really into it

The irony here is not as much in the results as it is in the authors.

Esleta claims to have just ‘ended up solving’ the problem, it being assigned earlier to an undergraduate student he co-advises. He still refers to the liquid-solid transition in granular media as his ‘original work’ in complexity science.

Monterola, on the other hand, is a neural networks expert, and one active complex systems researcher interested in a whole wide range of natural and social phenomena. The work with Esleta is one of his earliest publications upon return from post-doctoral work.

As with the trade-off between comfort and durability, Esleta adds another facet: that of style. In and outside the lab, prior to and after this research, this seems to be the aspect of clothing he’s more into. ■

1. Esleta, G.A.P. and Monterola, C.P. (2008). Structural reinforcement in a spring-block model of stress-induced fracture propagation. Computer Physics Communications, doi:10.1016/j.cpc.2007.12.003.
2. Esleta, G.A.P. and Monterola, C.P. (2008). Proceedings of the 25th Samahang Pisika ng Pilipinas Congress.

Segregation by heating

Short time scale segregation by convection

Industrial applications of granular material research involve studies of mixing and demixing behavior of mixtures of grains of various sizes and properties. Completely mixed cement, sand and gravel in the right proportions is vital in construction, while segregation is important in handling chemicals and drugs.

This led to a surge in the number of granular materials research aiming to quantify the conditions needed for segregation and/or mixing. Rotating or vibrated tumblers have been shown to produce either phenomena for particular values of frequencies or under special configurations (e.g. baffled tumblers). But there is yet another possible driver of segregation or mixing that is relatively untouched: the convection cells of made by a fluid heated at the bottom and cooled at the top. The regularity in the vortex motion of the fluid may aid in separating components of a granular mixture suspended in it.

This is the main point of a recent paper by Felix Valenzuela and Christopher Monterola, physics researchers at the National Institute of Physics in the University of the Philippines Diliman. Valenzuela, who will be defending his MS Physics thesis this semester, wrote the paper titled "Convective flow-induced short timescale segregation in a dilute bidisperse particle suspension", accepted for publication in the International Journal of Modern Physics C [1].

When a fluid (say, water) is heated at the bottom and cooled at the top and it reaches a critical condition called the critical Rayleigh number, it forms a vortex motion because the warm fluid below rises and, upon cooling at the top, eventually sinks. Seen from the side, it forms symmetrical circular motion, one clockwise and the other counter-clockwise.

While the effect of the particles on the fluid - namely, to change the direction of motion of the vortex - is investigated in a similar paper [2], the segregating effect of the fluid motion on the particles have only been described in Valenzuela's work. For very short time scales, initially mixed particles at the bottom of the tank undergo separation, due to the faster motion of light particles as compared with the heavier ones.

The paper used two measures to describe the separation of the particles: the index of dissimilarity, first used in the social sciences in describing how mixed populations are spatially in terms of races; and the entropy, a general measure of "disorder" in a system. Used together, these measures better describe the dynamics of mixing and demixing in time.

The paper is a first approximation, primarily because the particles used in the simulation have no physical dimension. Moreover the fluid-particle interaction is one-way: only the fluid imparts momentum into the particle. But in real systems particles do have geometrical differences, and they give a "kick" to the liquid upon moving.

Additional simulations are underway. The next step is to conduct actual experiments to further strengthen their claims. Will there be a cycle of mixing-demixing, as their earlier plots suggest? Is total segregation possible? These are some of the unanswered questions that the researchers aim to answer. But with the way things are going, they are positive they can replicate their interesting results and provide better insights into this phenomenon.

1. Valenzuela, J.F. and Monterola, C. (2008). Convective flow-induced short timescale segregation in a dilute bidisperse particle suspension. Accepted for publication in International Journal of Modern Physics C.
2. Bin Liu and Jun Zhang (2006). Self-Induced Cyclic Reorganization of Free Bodies Through Thermal Convection. Phys. Rev. Lett. 100: 244501.

The social network aspect of business competition

How friendship connection can be used for business growth

Typical school age kids would rather busy themselves with Facebook or Friendster than deal with more serious stuff like business. Interestingly, even more "mature" and "serious" people who deal with business should do too, according to a recent independent research by Erika Fille Legara, Anthony Longjas and Rene Batac, a team of PhD Physics students from the University of the Philippines.

In a paper titled "Competition in a Social Structure" to appear in the International Journal of Modern Physics C, the group quantified the extent at which social relationships affect economic choices, particularly in the use of mobile phones [1]. The research applies very aptly so in the Philippines, where SMS is most voluminous in the world, and where competition is practically between the two largest companies, Globe Telecommunications and Smart Communications.

Friendship connections

Mobile phone subscription is primarily dictated by the need to communicate and stay connected with family and friends. This, in itself, makes clear the notion that there really is a social relationship aspect to cellular phone use.

From this cue, the authors investigated the effect of friends and family relations to the growth of mobile phone companies in the Philippines. With a complex systems background, the team is familiar with the notion of the "degree distribution" within a real-world network: degree is the number of friends, and by the obvious fact that not all people have the same number of friends, the resulting histogram of the number of firends will follow a Brody distribution [2].

Each individual, therefore, is affected by the majority of his/her own little neighborhood, not by the global dynamics. It is possible to have an individual using a "less popular" mobile subscription because majority of his/her friends subscribe to that service.

Company growth

With data of mobile phone users for the last few years, the group is now ready to test their predictions.

They plotted the solution to a coupled differential equation describing the rate of company growth for both Globe and Smart and superimposed it with data provided by the National Telecommunications Commission (NTC) of the Philippines. The results - a perfect fit.

The differential equation model is based on continuum and mean-field approximations and with the assumption of a constant population with static friendships. The good correspondence of model results with data for the years 2001-2007 show that the assumptions used are valid. With this, the trend of increase in population of users for both networks are predicted for the coming years, with Smart leading and Globe following closely behind. Both are shown to have increasing trends for the next few years, albeit at slower rates.

As a conclusion, the authors suggested that strategies that target GROUPS of individuals instead of random individuals better in attracting more subscribers and, ultimately, winning in the competition.

In general the competition model proposed was shown to be general enough and can be applied to a wide range of other systems that are competing for resources that are spatially arranged in a network structure. Language death dynamics, for example, is included as an exmple in the paper.

Friends themselves

The authors are friends themselves, driven by a common interest in complex systems research.

What started out as a class project ended up as an independent publication by the group, who belong to different subgroups of complex systems research in the National Institute of Physics, UP. Erika studies network dynamics, while Anthony and Rene do granular materials experiment and modeling, respectively.

1. Legara, E.F.T., Longjas, A., and Batac, R. (2008). Competition in a Social Structure. To appear in International Journal of Modern Physics C. [pdf]
2. Lind, P.J. and Herrmann, H.J. (2007). New approaches to model and study social networks. New Journal of Physics 9, 228.

Deal or no deal? Physics looks into multi-level marketing

Growth and profitability in a directed business network

The promise of exponential growth by multi-level marketing (MLM) enterprises led to its continued presence (and even proliferation) in the Philippines. The general public is interested in the potential profitability. Government officials are wary of possible pyramid scheming. But how profitable really are MLM businesses, and just exactly how safe it is to join one?

In an attempt to provide a quantitative answer, a team of complex systems researchers from the Instrumentation Physics Laboratory combined analytic formulation, agent-based models, and real MLM data in a paper published in Physica A [1].

MLM architecture: Unilevel vs. binary

When asked what drives people to join MLM's, Erika Fille Legara, the main author, replies: "It's very lucrative and it promises high returns with only little investment. And you're your own boss. In a sense you're self employed."

MLM business enterprises require two things: (1) the products to sell; and (2) a network of downlines, or recruited individuals, to whom the products will be sold. Based on the latter, the MLM can be classified as either binary (each member is allowed only two direct downlines) or unilevel (no limit in direct downlines).

Earnings also come from these two pre-requisites, in the form of profits from the products and commissions for each recruited member. The balance between these two earning mechanisms is what sets MLM's apart from pyramid schemes; 70% of the earnings must come from the products if a MLM enterprise is to be considered "legal".

The more, the merrier?

In spite of the existence of such regulatory measure, gaining profits from recruitment is still the main driver of MLM activity especially in the Philippines.

The popularity of MLM enterprises rests on their claim of "unbridled growth", i.e. exponential growth of downlines resulting into higher profits in terms of products and commissions.

To test if such really is the case, the researchers segmented the MLM into different levels and counted the population of members in these levels. The first level corresponds to the founder, the second level his/her first recruits, the third the new recruits of these direct recruits, and so on. If growth is to be unlimited, there should be a continuous and steady increase in population per level.

Both for unilevel and binary MLM's, Legara notes that "the growth stagnates contrary to their claims of unbridled growth." In fact, the number of members per level peaks at some level midway down the network. While those members on top may in fact continue to have higher profits, the members further down below do not share their happiness, as they find themselves just "buyers" and not really "sellers". This phenomenon is observed true for both simulation and real data.

I quit!

This disparity may lead to quitting, and, possibly, collapse of the network structure.

The difference between unilevel and binary MLM structures is even more highlighted in terms of the resilience of the network and its robustness to random quitting. In general, unilevel structures are more prone to collapse due to random quitting than binary ones.

MLM's with binary network structure give pairing bonuses for every complete pair of downlines a recruiter has made. This provision, which is obviously not found in the unlimited-downline format of unilevel businesses, serves as a "healing mechanism" according to Legara. In terms of robustness to quitters, "more robust iyong binary (binary [MLM] is more robust)."

Leader vs. follower

The findings suggest that anybody interested in forming a new MLM network must choose a binary structure to resist collapse brought about by dissatisfied dropouts.

Forming a MLM business is entirely different from joining one. Asked whether she will join a MLM herself, Legara admits her decision "depends on the kind. If it's based solely on recruitment, then no. As you can see, the growth stagnates."

Membership in MLM is a risk: to see how much one can earn he/she must know where exactly he/she is in the heirarchy, an information MLM companies do not divulge. But of course, doing business is always a risk.


Of course, this research shed light only on quantitative aspects of MLM. There remains moral and ethical issues that need to be answered. These deeper problems will probably make complex systems researchers like Legara and her group busy next.

1. Legara, E.F.T., Juanico, D.E., Monterola, C.P., Palima, M.L. and Saloma, C.A. (2008). Earning potential in multi-level marketing enterprises. Physica A.