Works in Progress
I am currently thinking primarily about the resilience of road
infrastructure and, more specifically, about how that resilience
can be quantified in a meaningful and usable way. This line of
work feels important to me because it asks not only how roads
fail, but how they endure, adapt, and recover under changing
environmental and service conditions.
Virginia Tech has been a very good place to pursue these
questions. I am grateful for the opportunity to work here, and I
have especially benefited from the guidance of Professor Deb
Mishra, whose clarity, sharpness, and communicative style make
him an excellent mentor and a deeply thoughtful person to learn
from. In some ways, he reminds me of my previous supervisor,
Professor Dharamveer Singh, who was also exceptionally sharp,
intelligent, and full of promise.
A Technical Note
Ways of Reading Asphalt Binder
-
SARA Fractionation (Iatroscan)
Function: Separates asphalt into four
chemical families based on solubility and polarity:
Saturates, Aromatics, Resins, and Asphaltenes.
What it gives us: The colloidal index. It
tells us how well the asphaltenes, the hard and brittle
parts, are dispersed in the maltenes, the softer and oilier
parts. This helps predict whether a binder will remain stable
or phase-separate and become brittle.
-
FTIR (Fourier Transform Infrared Spectroscopy)
Function: Measures how the binder absorbs
infrared light at different wavelengths to identify specific
functional groups.
What it gives us: Oxidation indices,
especially carbonyl and sulfoxide peaks. It is the primary
tool for measuring how much a binder has aged or rusted at a
molecular level because of heat and oxygen.
-
GPC / SEC (Gel Permeation Chromatography)
Function: Acts like a molecular sieve that
separates molecules by size.
What it gives us: The molecular weight
distribution. It identifies the formation of large molecular
size particles, which increase as asphalt ages, and it is
also excellent for confirming the presence of polymers such
as SBS.
-
DSC (Differential Scanning Calorimetry)
Function: Measures the amount of heat
absorbed or released by the binder as it is heated or cooled.
What it gives us: The glass transition
temperature \(T_g\) and wax content. It identifies the
temperature at which the binder turns from a flexible
material into a brittle, glassy state, which is critical for
cold-weather performance.
-
CHNS (Elemental Analysis)
Function: Completely combusts a tiny sample
to determine the mass percentage of carbon, hydrogen,
nitrogen, and sulfur.
What it gives us: The elemental profile. A
high sulfur content, for example, often points to specific
crude oil sources, including those from the Middle East,
while the carbon-to-hydrogen ratio can indicate the degree of
aromaticity.
-
NMR (Nuclear Magnetic Resonance)
Function: Uses a strong magnetic field to
observe the environment of hydrogen or carbon atoms.
What it gives us: Aromatic and aliphatic
carbon content. It provides a much more detailed skeleton map
of the molecules than FTIR, allowing researchers to see how
the carbon chains are actually structured.
-
XRF (X-Ray Fluorescence)
Function: Bombards the sample with X-rays to
cause the emission of characteristic secondary X-rays from
metals.
What it gives us: Trace metal detection. It
is used to find zinc, copper, or molybdenum, which can act as
fingerprints for recycled engine oil bottoms or other
prohibited additives.
-
AFM (Atomic Force Microscopy)
Function: Scans a physical probe over the
surface of the binder to map its topography at the nanoscale.
What it gives us: Micro-morphology, often in
the form of bee structures. It shows the distribution of wax
and asphaltenes on the surface, which relates to how the
binder will adhere to aggregates.
-
Fluorescence Microscopy
Function: Uses high-intensity UV light to
make certain materials glow.
What it gives us: Polymer dispersion quality.
Since most polymers used in asphalt glow under UV light while
the bitumen remains dark, this test shows whether the polymer
is blended evenly or forming large, inefficient clumps.
Convolutional neural networks as an entry point into modern
machine learning.
Machine learning has changed dramatically in recent years,
especially with the rise of artificial neural networks. These
biologically inspired computational models now outperform many
earlier forms of artificial intelligence across a wide range of
learning tasks.
Among the most influential neural network architectures is the
convolutional neural network, or CNN. CNNs are particularly
powerful for image-based pattern recognition, and their
relatively clear structure makes them one of the most accessible
ways to begin working with modern neural networks.
At this stage, my interest in CNNs is mainly directed toward
understanding how the architecture developed, how it is being
used in current work, and what kinds of image-recognition
problems it handles especially well.
I am reading on CNNs at the moment because I expect to use them
in my current work, and I want to build that understanding from
the basics upward rather than treating them as a black box.
A useful starting point, and a gentle introduction for readers
who want an entry into CNNs, is
arXiv:1511.08458.
Why is Perelman awesome?
Grigori Perelman
A figure who remains very much on my mind is Grigori
Perelman, whose intellectual courage, depth, and refusal of
spectacle continue to feel extraordinary. He represents, to
me, a rare model of what it means to pursue ideas with
absolute seriousness and without compromise.
I am also planning to read Perfect Rigor, which
feels like a natural way to stay with his work and the
strange clarity surrounding his life.
Book:
Perfect Rigor: A Genius and the Mathematical Breakthrough
of the Century
(link)
Current Curiosity
Rayleigh Distribution and the Stress-Strain Curve
I want to spend time on the Rayleigh
distribution and the stress-strain curve, especially as a way of
thinking more carefully about variability, response, and the shape
of material behavior under loading. What interests me here is not
only the mathematics itself, but also the possibility of seeing
statistical description and mechanical interpretation in a more
connected way.
A Thought
Rheology, Theology, and the Deborah Number
There is a strange parallel
between rheology and theology through the Deborah number. The
biblical line often paraphrased as “the mountains flowed before
the Lord” takes on an entirely different force once one remembers
that, given enough time, even what appears solid may begin to
move. In that sense, the Deborah number feels like more than a
technical ratio; it becomes a reminder that permanence is often a
matter of timescale. Howard A. Barnes and his colleagues discuss this beautifully
in
An Introduction to Rheology, which is a book I love and keep returning to.
A Mathematical Aside
Erdos Number
Erdos number is quite interesting, partly
because it turns collaboration into something almost topological.
It is a playful concept, but it also says something serious about
how mathematical work travels through people, papers, and shared
intellectual lineages.
Formally, if we think of a collaboration graph \(G=(V,E)\), where
each author is a vertex and an edge joins two authors who have
written a paper together, then the Erdos number of an author
\(v\) is simply the graph distance from \(v\) to Paul Erdos:
\[
\operatorname{Erdos}(v)=d_G(v,\mathrm{Erdos}).
\]
In that sense, a whimsical academic fact becomes a clean
expression of connectedness inside a scholarly network. It also
reminds me of graph theory, which fascinates me. In that spirit,
Network Science
by Albert-László Barabási is a wonderful read.
A Mathematical Aside
Poisson Distribution
The Poisson distribution has a kind of austere elegance. It is
one of the cleanest ways to describe how often something happens
when events arrive rarely, independently, and with a steady
average rate. It feels modest at first, but it is one of those
formalisms that quietly appears everywhere.
If \(X\) counts the number of events in a fixed interval and
\(\lambda\) is the average rate, then the basic model is
\[
\Pr(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}, \qquad k=0,1,2,\dots
\]
The beauty of it is that one number, \(\lambda\), controls both
the expected count and the variance. In that sense, the Poisson
distribution is a compact way of saying: randomness can still
have shape, and even scattered events can obey a disciplined
pattern.
A Mathematical Aside
Graph Theory
I am quite genuinely infatuated with graph theory. There is
something deeply satisfying about the way it reduces structure,
relation, and complexity to a language that is both austere and
expansive. A graph can look minimal on paper, \(G=(V,E)\), and
yet carry within it connectivity, flow, distance, centrality,
cycles, spanning trees, and entire geometries of interaction.
At the most basic level, if \(V\) is a finite vertex set and
\(E \subseteq \{\{u,v\}:u,v\in V,\;u\neq v\}\), then a great deal
already follows. One may define the degree of a vertex
\(v \in V\) by
\[
\deg(v)=\lvert\{u\in V:\{u,v\}\in E\}\rvert,
\]
and the graph distance between two vertices \(u,v\in V\) by
\[
\begin{aligned}
d_G(u,v)=\min\{\ell:\;&\exists\text{ a path }\\
&u\leadsto v\text{ of length }\ell\}.
\end{aligned}
\]
From there the whole subject seems to open: connectedness becomes
a statement that \(d_G(u,v) < \infty\) for every pair of
vertices, a tree becomes a connected graph with \(|E|=|V|-1\),
and an adjacency matrix \(A=(a_{ij})\) encodes the graph in a
way that lets combinatorics and linear algebra speak to one
another through
\[
a_{ij}=
\begin{cases}
1, & \text{if } \{v_i,v_j\}\in E,\\
0, & \text{otherwise.}
\end{cases}
\]
What I love here is not only the formalism, though the formalism
is beautiful, but the fact that graphs keep reappearing
everywhere: collaboration networks, infrastructure systems,
transport problems, diffusion, reliability, and the movement of
ideas themselves. Graph theory feels to me less like a chapter of
mathematics and more like a durable way of seeing.
A Physical Reverie
Dirac and the Other Half
Dirac trusted an equation far enough to let it describe matter
that no one had yet seen. His union of quantum mechanics and
special relativity,
\[
\bigl(i\gamma^\mu\partial_\mu-m\bigr)\psi=0,
\]
carried solutions that seemed to point beyond the known world.
Rather than discard them as mathematical inconvenience, Dirac
followed their logic toward the positron and antimatter.
In that sense, Dirac conceived half of the material universe in
his mind before experiment revealed it. It remains one of the
loveliest examples of disciplined imagination: an equation
insisting that nature was larger, stranger, and more symmetrical
than anyone had observed.
A Reading Note
On the Importance of Reading
I keep returning to the importance of reading, not only as an
academic obligation but as a way of enlarging inner life,
sharpening judgment, and developing seriousness of thought. One
of the most memorable reminders of this comes from Werner Herzog,
whose relentless emphasis on reading feels both demanding and
liberating.
His repeated insistence to read, read, read says
something essential: intellectual work is not sustained by
information alone, but by long companionship with books, voices,
and ideas. He says this in the context of filmmaking, but it
applies just as strongly to research, where depth of thought is
often inseparable from depth of reading. This
compilation
of Herzog on reading is something I find genuinely awesome.
An Eclipse, A Verdict
Eddington and the Bent Light
Einstein's general theory of relativity made a precise and
audacious prediction: the Sun's gravity should bend passing
starlight, shifting the apparent position of a star near the
solar limb by
\[
\Delta\theta=\frac{4GM_{\odot}}{c^2b}\approx1.75^{\prime\prime}.
\]
During the total solar eclipse of 29 May 1919, Arthur Eddington
photographed stars from Príncipe while a companion expedition
observed from Sobral, Brazil. With the Sun briefly hidden, the
sky became a laboratory: the stars appeared displaced by the
curvature through which their light had travelled.
The results announced by Frank Dyson, Eddington, and Andrew
Crommelin were consistent with Einstein's prediction and became
the celebrated first observational confirmation of general
relativity. I find the scene irresistible: an eclipse made the
geometry of spacetime visible, and an idea formed in equations
left a measurable mark upon the sky. The Royal Astronomical
Society preserves an excellent
account of the eclipse.
A Scenario Worth Stress-Testing
AI 2040: A Future Delayed on Purpose
The AI Futures Project's AI 2040: Plan A is not
presented as its authors' most likely forecast. It is a
positive policy scenario: slow the race to superintelligence,
make frontier research inspectable, and preserve human control
long enough to build a credible safety case.
Read AI 2040 →
-
2029
Make the deal
The United States and China agree to a verified slowdown and
declare the compute that could sustain frontier development.
-
2030
Brake the loop
Fully automated AI research would trigger a rapid takeoff;
the agreement prevents that loop while useful inference
remains available.
-
2035
Hold the line
Development pauses near top-human-expert capability, creating
time for alignment, oversight, and institutional learning.
-
2040
Conditional handoff
Scaling resumes toward superintelligence only after confidence
in safety is judged stronger than the risks of waiting.
01
Verify the compute
Chip accounting, mutual declarations, audits, inference-only
controls, and secured research clusters make the slowdown
enforceable without relying on trust alone.
02
Open the research
Algorithms, experiments, code, and safety cases become open
to scrutiny, while dangerous model weights and sensitive data
remain protected.
03
Titrate capability
Scale toward the strongest AI that remains confidently
controllable, then slow almost to a halt rather than racing
through an intelligence explosion.
The five pressures Plan A confronts
- Loss of control
- Concentrated power
- Great-power conflict
- Labor displacement
- Catastrophic misuse
What interests me most is the discipline of scenario scrutiny.
Instead of saying that governance will somehow catch up, the
proposal has to survive dates, incentives, verification limits,
institutional weakness, and the possibility of defection. Whether
or not one accepts Plan A, that is a serious way to think about a
future arriving faster than our institutions can comfortably
reason about it.