PostPoems Be Artistic. Be Creative. Be Inspired!

Prelude: On May 7th 2021, someone brutally murdered my beautiful Miss Millie. It was so horrid they wouldn’t let me see her body. Just so you can appreciate the horror, I couldn’t retrieve her collar and tag as I was told it was “too confronting” for both me and the staff. I had to weep and mourn over her semi-frozen corpse. On the RSPCA’s recommendation, I ordered a necropsy. I was told by the vet who conducted the necropsy, for my own sanity, not to read the results. They were correct. I shouldn’t have. But, of course, I did.

Skip forward to today. I am still mourning the death of my almost 17-year-old rescue cat, Mr Kitty, after a battle with cancer. I am also trying to deal with my other rescue cat, Boudica, a Tonkinese, who turned suddenly anorexic on Friday. Is it depression from losing Mr Kitty, or is it a relapse of the acute kidney injury (AKI) [previously known as acute renal failure] that almost took her life at Christmas/New Year?

Mr Kitty holding the remote while we waited for Boudica to be cleared from the veterinary hospital.

Using a combination of Nutripet and a high-energy nutrient gel that stimulates appetite, Hill’s Science kd wet food, there has been some improvement. She showed signs of her normal self when she waited outside the shower door to get wet skritches, then returned to my bed after having a good drink. Unfortunately, still nothing in any of the litter boxes other than pawprints.

Boudica in the Veterinary Hospital a few days before she was able to come home.

So this afternoon, suffering from exhaustion, depression and huge anxiety, I decided to spend the day in bed with Boudica. As we cuddle, I keep hearing footsteps. To me, they sound so much like that of Miss Millie when she would quietly creep into the bedroom and join all the cats and me for a group snuggle.

As carefully as I can to not disturb Boudica, I lift and turn my head and see, of course, nothing.

Intelligence would be recognising that the “footsteps” I hear are merely a product of thermal expansion and contraction.

Thermal expansion and contraction are thermodynamic phenomena governed by the principles of kinetic theory and molecular interactions. When a material experiences a temperature increase, the kinetic energy of its constituent particles rises, leading to greater amplitude vibrations and, subsequently, an increase in the average distance between particles. This is a macroscopic result of microscopic behaviours, where the lattice structures of solids expand; hence, we observe dimensional changes in the material.

In scenarios involving solid surfaces or mediums, such as a floor, thermal expansion can alter the structural integrity and integrity of the interface with other materials, such as air or footfalls. When a foot strikes the ground, the downward force causes localised stress, affecting the material’s microstructure. This stress can generate compression waves in the solid, propagating as longitudinal waves through the medium.

From a mathematical standpoint, the relationship between temperature variation and dimensional change can be expressed through the linear expansion formula:

ΔL=αΔTLo⇒Lf−Lo=αΔTLo⇒Lf=Lo(1+αΔT)

where ΔL is the change in length, α is the material’s coefficient of linear expansion, Lo is the original length, and ΔT denotes the change in temperature.

Moreover, thermodynamics can also address the specific heat capacity of materials, which necessitates energy transfer to increase the thermal agitation and lead to expansion. The propagation of sound originating from the footsteps is then modelled via the wave equation, considering parameters such as density, modulus of elasticity, and the speed of sound in the material medium.

In terms of thermodynamics, specific heat capacity (c) quantifies the amount of energy (Q) required to raise the temperature of a unit mass (m) of a material by one degree (ΔT). This relationship is described by the equation:

Q=mcΔT

This concept relates to the microscopic behaviour of particles, where energy transfer increases the thermal agitation of the material. This can be expressed through internal energy (U) or enthalpy (H) variations, depending on the system’s constraints. Additionally, sound wave propagation from footsteps can be modelled using the wave equation, typically expressed as:

∂²u/∂t² = c²∇ ²u

where u is the displacement field, c is the speed of sound in the medium, and ∇² represents the Laplacian operator, reflecting spatial variations in the medium’s displacement. The speed of sound (c) in a material is influenced by factors such as the material’s density (ρ) and its modulus of elasticity (E), with the relationship defined by:

c = sqrt E/ρ

Footsteps create pressure waves that travel through solids and air, allowing sound perception at varying distances depending on factors like temperature gradients, medium properties, and acoustic impedance mismatches. Consequently, the auditory perception of footsteps arises from a multifaceted interaction of thermal dynamics, material properties, and acoustic wave propagation. 

Yet, perhaps wisdom lies in the choice to believe those footsteps belong to my cherished Millie, gently coming to check on me because I long for her comforting love in this moment of need.